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Computer programming for robotics MCQ

1. What order does Householder's method achieve?

D - 1

D/2

D + 1

Answer

Correct Answer: D + 1

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2. What is polynomial interpolation?

A method of joining points

A method based on polynomials

A curve that connects points

A measure of central tendency

Answer

Correct Answer: A method based on polynomials

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3. What is the twiddle factor?

Trigonometric constant coefficients that are multiplied by the data

The exponential value of x

The hypotenuse of a right triangle

The angle of the radian

Answer

Correct Answer: Trigonometric constant coefficients that are multiplied by the data

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4. What is the bit-reversal permutation?

A process of reversing the bits in a binary number

A type of data compression algorithm

A process of converting a bitmap image into a vector graphic

A particular permutation of vectors with 2m entries used in many FFTs.

Answer

Correct Answer: A particular permutation of vectors with 2m entries used in many FFTs.

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5. What is the split-radix FFT algorithm?

An algorithm for the multiplication of large integers

An algorithm for the factorization of polynomials

An algorithm that is used to compute the discrete Fourier transform (DFT)

Variant of Cooley– Tukey that uses a blend of radices 2 and 4

Answer

Correct Answer: Variant of Cooley– Tukey that uses a blend of radices 2 and 4

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6. What is the Fast Fourier Transform?

The inverse of the discrete Fourier transform

A method for computing the Fast Fourier Transform

A fast method for computing the discrete Fourier transform

A method for computing the discrete Fourier transform

Answer

Correct Answer: A fast method for computing the discrete Fourier transform

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7. What is the Discrete Fourier transform?

Extrapolation at equidistant points

Transformation at equidistant points

Interpolation at non-equidistant points

Trigonometric interpolation at equidistant points

Answer

Correct Answer: Trigonometric interpolation at equidistant points

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8. What is trigonometric interpolation?

A process of estimating values that lies between known values

Interpolation by trigonometric polynomials

A method of approximating values of functions between known data points

A process of constructing new data points within the range of a discrete set of known data points

Answer

Correct Answer: Interpolation by trigonometric polynomials

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9. What is Blossom?

A curve that represents the variation of a quantity

A mathematical function that is used to approximate a real-valued function

A unique, affine, symmetric map associated to a polynomial or spline

A graph with coordinates that determine the shape of a curve

Answer

Correct Answer: A unique, affine, symmetric map associated to a polynomial or spline

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10. What is a smoothing spline?

A spline that interpolates between data points

A spline fitted smoothly to noisy data

A spline that does not pass through all data points

A spline with sharp bends

Answer

Correct Answer: A spline fitted smoothly to noisy data

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11. What is an I-spline?

A non-monotone spline, not defined in terms of M-splines

A non-monotone spline, defined in terms of M-splines

A monotone spline, not defined in terms of M-splines

A monotone spline, defined in terms of M-splines

Answer

Correct Answer: A monotone spline, defined in terms of M-splines

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12. M-spline is a type of spline that is _____.

Negative

Non-negative

Positive

Zero

Answer

Correct Answer: Non-negative

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13. What is a coons patch?

A patch of land set aside for raccoons

A type of manifold parametrization used to smoothly join other surfaces together

The place where raccoons live

A fabric made from the fur of raccoons

Answer

Correct Answer: A type of manifold parametrization used to smoothly join other surfaces together

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14. What is De Boor's algorithm?

A method of solving systems of linear equations

De Casteljau's algorithm

A method for approximating definite integrals

A root-finding algorithm

Answer

Correct Answer: De Casteljau's algorithm

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15. What is a box spline?

A multivariate generalization of B-splines

A mathematical function

A method of interpolation

A type of regression analysis

Answer

Correct Answer: A multivariate generalization of B-splines

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16. What does Bézier surface do?

Maps a triangle to R2.

Maps a circle to R2.

Maps a square to R3.

Find the area of a triangle

Answer

Correct Answer: Maps a square to R3.

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17. What does the Bézier triangle do?

Maps a circle to R3

Maps a triangle to R2

Maps a triangle to R3

Maps a square to R3

Answer

Correct Answer: Maps a triangle to R3

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18. The volume of a rectangular box is found by multiplying which two dimensions?

Width and height

Length and height

Length and width

All three dimensions

Answer

Correct Answer: Length and width

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19. The number of dimensions in which a manifold can be embedded in a Euclidean space is called its?

Its domain

Its codimension

Its dimension

Its range

Answer

Correct Answer: Its codimension

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20. What is the centripetal Catmull–Rom spline?

Catmull–Rom surface

Catmull–Clark subdivision surface

Catmull–Rom curve

Special case of cubic Hermite splines without self-intersections or cusps

Answer

Correct Answer: Special case of cubic Hermite splines without self-intersections or cusps

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21. What is a perfect spline?

A polynomial spline of degree 1

A polynomial spline of degree 2

A polynomial spline of degree 3

A polynomial spline of degree m whose mth derivate is ± 1

Answer

Correct Answer: A polynomial spline of degree m whose mth derivate is ± 1

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22. What is a Spline?

A exponential

A piecewise polynomial

A logarithm

A polynomial

Answer

Correct Answer: A piecewise polynomial

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23. What is the Padua points?

They are a ancient folk band from Wales

A set of points in R2 with unique polynomial interpolant and minimal growth of Lebesgue constant

A football team from Italy

A type of pasta dish from Italy

Answer

Correct Answer: A set of points in R2 with unique polynomial interpolant and minimal growth of Lebesgue constant

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24. How many dimensions do we live in?

Answer

Correct Answer: 3

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25. In mathematics, what is the name given to a number that represents a quantity along a line?

Real number

Complex number

Imaginary number

Scalar

Answer

Correct Answer: Real number

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26. What is Brahmagupta's interpolation formula?

A method for finding the roots of a polynomial

A formula for estimating the value of a polynomial at a certain point

A seventh-century formula for quadratic interpolation

A method for approximating the value of a polynomial at a certain point

Answer

Correct Answer: A seventh-century formula for quadratic interpolation

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27. What is the Bernstein polynomial used for?

Subtraction

Approximation

Multiplication

Addition

Answer

Correct Answer: Approximation

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28. What is Neville's algorithm?

For approximating a function from a set of data points; based on the least squares method

For approximating a definite integral; based on the trapezoidal rule

For evaluating the interpolant; based on the Newton form

For approximating a definite integral; based on the midpoint rule

Answer

Correct Answer: For evaluating the interpolant; based on the Newton form

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29. What is the interpolant?

A mathematical function that connects discrete points with a smooth curve

A mathematical function that connects discrete points with a sharp curve

A mathematical function that connects discrete points with a wavy curve

A mathematical function that connects discrete points with a jagged curve

Answer

Correct Answer: A mathematical function that connects discrete points with a smooth curve

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30. What is Nearest-neighbor interpolation?

A method of estimating values that is used when the exact value is not known

An estimation method used when interpolating between two known values

Taking the value of the nearest neighbor

A mathematical process used to predict unknown values

Answer

Correct Answer: Taking the value of the nearest neighbor

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31. What is interpolation?

Linear regression

Polynomial

Extrapolation

Construct a function going through some given data points

Answer

Correct Answer: Construct a function going through some given data points

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32. What are matrix-free methods?

Methods that only access the matrix by evaluating vector-vector products

Methods that only access the matrix by evaluating matrix-vector products

Methods that only access the matrix by evaluating matrix-matrix products

Methods that only access the matrix by evaluating matrix-matrix and vector-vector products

Answer

Correct Answer: Methods that only access the matrix by evaluating matrix-vector products

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33. What is a pivot element?

A random element in the matrix

The last element in the matrix

The first element in the matrix

Entry in a matrix on which the algorithm concentrates

Answer

Correct Answer: Entry in a matrix on which the algorithm concentrates

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34. What is in-place matrix transposition?

Computing the transpose of a matrix without using much additional storage

Not computing the transpose of a matrix

Using additional storage to compute the transpose of a matrix

Computing the transpose of a matrix

Answer

Correct Answer: Computing the transpose of a matrix without using much additional storage

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35. What does the Cuthill-McKee algorithm do?

Finds the inverse of a matrix

Permutes rows/columns in sparse matrix to yield a narrow band matrix

Multiplies two matrices

Generates a permutation matrix

Answer

Correct Answer: Permutes rows/columns in sparse matrix to yield a narrow band matrix

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36. What is the analogue of Householder transformation for general inner product spaces?

Householder reflection

Householder permutation

Householder matrix

Householder operator

Answer

Correct Answer: Householder operator

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37. What are Orthogonalization algorithms?

A class of algorithms used to calculate the orthogonal projection of a vector onto a subspace

A set of points with equal distances from each other

A set of points that form a right angle

A set of points that lie on the same line

Answer

Correct Answer: A class of algorithms used to calculate the orthogonal projection of a vector onto a subspace

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38. What is the Eigenvalue perturbation?

A measure of how close two matrices are

A type of matrix

A way to calculate eigenvalues

Stability of eigenvalues under perturbations of the matrix

Answer

Correct Answer: Stability of eigenvalues under perturbations of the matrix

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39. What does the acronym LOBPCG stand for?

Locally Optimal Blocked Conjugate Gradient Method

Locally Optimal Block Partitioned Conjugate Gradient Method

Locally Optimal Block Preconditioned Conjugate Gradient Method

Linear Optimal Block Preconditioned Conjugate Gradient Method

Answer

Correct Answer: Locally Optimal Block Preconditioned Conjugate Gradient Method

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40. What is the Jacobi eigenvalue algorithm?

A method for exponentiating a matrix

A method for calculating the inverse of a matrix

A method for approximating the eigenvalues of a matrix

A method for diagonalizing a matrix

Answer

Correct Answer: A method for approximating the eigenvalues of a matrix

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41. What is the Block Lanczos algorithm used for?

When matrix is over a finite field

When matrix is over an infinite field

When matrix is over a complex field

When matrix is over a real field

Answer

Correct Answer: When matrix is over a finite field

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42. What is the Lanczos algorithm specialized for?

Special matrices

Positive matrices

Definite matrices

Positive-definite matrices

Answer

Correct Answer: Positive-definite matrices

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43. What is Arnoldi iteration?

A method for solving nonlinear systems of equations that are too large to be handled by direct methods

A numerical technique for approximating the eigenvalues and eigenvectors of a large matrix

A method for solving linear systems of equations that are too small to be handled by direct methods

A method for solving linear systems of equations that are too large to be handled by direct methods

Answer

Correct Answer: A method for solving linear systems of equations that are too large to be handled by direct methods

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44. What is the Eigenvalue algorithm?

A numerical algorithm for locating the eigenvalues of a vector

A numerical algorithm for locating the eigenvectors of a vector

A numerical algorithm for locating the eigenvalues of a matrix

A numerical algorithm for locating the eigenvectors of a matrix

Answer

Correct Answer: A numerical algorithm for locating the eigenvalues of a matrix

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45. What does 'sparse approximation' mean?

Find the most precise solution

Find the sparsest solution

Find the most optimal solution

Find the most efficient solution

Answer

Correct Answer: Find the sparsest solution

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46. What is the sparsest solution?

The solution with as many threes as possible.

The solution with as many zeros as possible.

The solution with as many twos as possible.

The solution with as many ones as possible.

Answer

Correct Answer: The solution with as many zeros as possible.

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47. What is the Moore-Penrose pseudoinverse used for?

For finding the solution with the largest residual

For finding the solution with the smallest 2-norm

For finding the solution with the smallest residual

For finding the solution with the largest 2-norm

Answer

Correct Answer: For finding the solution with the smallest 2-norm

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48. What is the numerical computation of null space?

Find no solutions of an underdetermined system

Find only one solution of an underdetermined system

Find all solutions of an underdetermined system

Find all solutions of an overdetermined system

Answer

Correct Answer: Find all solutions of an underdetermined system

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49. How many solutions does an overdetermined system have?

Zero

Two

More than one

One

Answer

Correct Answer: More than one

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50. What is Uzawa iteration?

A method for solving saddle node problems

A method for solvingDiscrete Logarithm Problems

A method for solving linear programming problems

A numerical analysis technique for solving systems of linear equations

Answer

Correct Answer: A method for solving saddle node problems

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51. What does LU factorization refer to?

Partial LU factorization

LU decomposition

LU matrix factorization

Sparse approximation to the LU factorization

Answer

Correct Answer: Sparse approximation to the LU factorization

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52. What is Stone's method?

A method that uses an incomplete LU decomposition

A method of graphing linear equations

A method of factoring polynomials

A method of solving systems of linear equations

Answer

Correct Answer: A method that uses an incomplete LU decomposition

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53. What does SIP stand for in Stone's method?

Successive Interpolation Procedure

Standard Interpolation Procedure

Strongly Implicit Procedure

Simple Implicit Procedure

Answer

Correct Answer: Strongly Implicit Procedure

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54. What does Chebyshev iteration avoid?

Numerical quadrature

Inner products

Need for matrix inversion

Solution to the system of linear equations

Answer

Correct Answer: Inner products

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55. What is the GMRES method based on?

Conjugate gradient method

Gauss–Seidel method

Arnoldi iteration

Gradient descent method

Answer

Correct Answer: Arnoldi iteration

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56. Which of the following is true about the Conjugate residual method?

It is similar to CG but only assumed that the matrix is invertible.

It is similar to CG but only assumed that the matrix is diagonal.

It is similar to CG but only assumed that the matrix is symmetric.

It is similar to CG but only assumed that the matrix is positive definite.

Answer

Correct Answer: It is similar to CG but only assumed that the matrix is symmetric.

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57. What is Biconjugate gradient stabilized method?

A type of dance

A color

Variant of BiCG with better convergence

A mathematicians

Answer

Correct Answer: Variant of BiCG with better convergence

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58. What is the Nonlinear Conjugate Gradient Method?

A method for solving nonlinear optimization problems

A method for solving problems with linear equations

A generalization for nonlinear optimization problems

A method for solving linear optimization problems

Answer

Correct Answer: A generalization for nonlinear optimization problems

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59. Conjugate gradient method assumes which of the following?

Symmetric

Positive semidefinite

Positive definite

Hermitian

Answer

Correct Answer: Positive definite

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60. What is a Backfitting algorithm?

Data mining technique

Machine learning algorithm

Optimization algorithm

Iterative procedure used to fit a generalized additive model, often equivalent to Gauss–Seidel

Answer

Correct Answer: Iterative procedure used to fit a generalized additive model, often equivalent to Gauss–Seidel

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61. Backfitting algorithm is used to fit which type of model?

Holdout cross-validation

Hoeffding's lemma

Generalized additive model

Geometric model

Answer

Correct Answer: Generalized additive model

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62. What is SSOR?

Symmetric split-operator representation

Symmetric surrogate operator representation

Symmetric successive over-relaxation

Symmetric sigma-operator representation

Answer

Correct Answer: Symmetric successive over-relaxation

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63. What is Symmetric successive over-relaxation?

SSOR matrices are always symmetric.

SSOR is a variant of SOR for non-symmetric matrices.

SSOR was created to solve the SOR problem for symmetric matrices.

SSOR is a variant of SOR for symmetric matrices.

Answer

Correct Answer: SSOR is a variant of SOR for symmetric matrices.

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64. What does Cyclic reduction do?

Cyclic reduction increases data

Cyclic reduction eliminates even or odd rows or columns, and then repeats the process.

Cyclic reduction randomizes data

Cyclic reduction decreases data

Answer

Correct Answer: Cyclic reduction eliminates even or odd rows or columns, and then repeats the process.

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65. What is SPIKE algorithm?

Hybrid parallel solver for narrow-banded matrices

Hybrid parallel solver for matrices

Parallel solver for narrow-banded matrices

Algorithm for solving matrices

Answer

Correct Answer: Hybrid parallel solver for narrow-banded matrices

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66. What is Levinson recursion?

A method for computing the determinant of a Toeplitz matrix

A method for computing the inverse of a matrix

A method for solving linear system of equations

A method for computing the inverse of a Toeplitz matrix

Answer

Correct Answer: A method for computing the inverse of a Toeplitz matrix

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67. What is nested dissection?

A symmetric matrix

A method for symmetric matrices, based on graph partitioning

A method for asymmetric matrices, based on graph partitioning

A partitioning of a graph

Answer

Correct Answer: A method for symmetric matrices, based on graph partitioning

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68. What is a frontal solver?

A method used in finite element methods

A device that measures wind speed

A software that helps create 3D models

A type of 3D printer

Answer

Correct Answer: A method used in finite element methods

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69. What is the meaning of "iterative refinement"?

A method of problem-solving

A way to design algorithms

A procedure to turn an inaccurate solution in a more accurate one.

A programming technique

Answer

Correct Answer: A procedure to turn an inaccurate solution in a more accurate one.

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70. What is Cholesky decomposition used for?

Solving a system with a non-square matrix

Solving a system with a positive definite matrix

Solving a triangular linear system of equations

Solving a system with a negative definite matrix

Answer

Correct Answer: Solving a system with a positive definite matrix

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71. What does the Bareiss algorithm do?

It is used to solve systems of linear equations

It is used to find the inverse of a matrix

It ensures that all entries remain integers if the initial matrix has integer entries

It minimizes the number of operations needed to compute the determinant of a matrix

Answer

Correct Answer: It ensures that all entries remain integers if the initial matrix has integer entries

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72. What is a row echelon form?

A matrix in which all entries below a nonzero entry are zero

A matrix with each row having exactly one nonzero entry

A matrix in which all entries above a nonzero entry are zero

A matrix with only one nonzero entry

Answer

Correct Answer: A matrix in which all entries below a nonzero entry are zero

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73. What is matrix splitting?

Expressing a given matrix as a sum or difference of matrices

Expressing a given matrix as a product of matrices

Expressing a given matrix as a sum or difference of vectors

Expressing a given matrix as a function of matrices

Answer

Correct Answer: Expressing a given matrix as a sum or difference of matrices

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74. What is the Singular Value Decomposition?

Unitary matrix times diagonal matrix times unitary matrix

A matrix that can be used to transform one vector into another

A method for solving linear least squares problems

A mathematical process for solving systems of linear equations

Answer

Correct Answer: Unitary matrix times diagonal matrix times unitary matrix

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75. What is the Jordan–Chevalley decomposition?

Sum of commuting nilpotent matrix and diagonalizable matrix

Subtraction of a nilpotent matrix from a diagonalizable matrix

Addition of a nilpotent matrix and a diagonalizable matrix

Multiplication of a nilpotent matrix and a diagonalizable matrix

Answer

Correct Answer: Sum of commuting nilpotent matrix and diagonalizable matrix

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76. What is Weyr canonical form?

Addition of two matrices

A sequence of linear transformations that converts a matrix to Jordan normal form

Permutation of Jordan normal form

The set of all invertible matrices

Answer

Correct Answer: Permutation of Jordan normal form

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77. What is Jordan normal form?

A diagonal matrix

An identity matrix

A bidiagonal matrix of a certain form

A triangular matrix

Answer

Correct Answer: A bidiagonal matrix of a certain form

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78. What is Eigendecomposition?

Decomposition in terms of physics

Decomposition in terms of eigenvectors and eigenvalues

Decomposition in terms of chemistry

Decomposition in terms of mathematics

Answer

Correct Answer: Decomposition in terms of eigenvectors and eigenvalues

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79. What does DBSM stand for?

Data by similarity

Decomposers by similarity

Decomposition by sampling

Decompositions by similarity

Answer

Correct Answer: Decompositions by similarity

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80. What is the Polar decomposition?

Unitary matrix times positive-semidefinite Hermitian matrix

A type of decomposition that only happens in cold climates

A process of breaking down a substance

The splitting of a molecule into two equal parts

Answer

Correct Answer: Unitary matrix times positive-semidefinite Hermitian matrix

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81. What is RRQR factorization?

QR factorization

Reduced row echelon form

Rank-revealing QR factorization

Echelon form

Answer

Correct Answer: Rank-revealing QR factorization

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82. Can RRQR factorization be used to compute the rank of a matrix?

Only for square matrices

Yes

Only for certain matrices

Answer

Correct Answer: Yes

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83. What is LU decomposition?

A way to factor a matrix

Lower triangular times upper triangular

A type of matrix

A method for solving linear equations

Answer

Correct Answer: Lower triangular times upper triangular

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84. What is Freivalds' algorithm?

A sorting algorithm

A division algorithm

A randomized algorithm for checking the result of a multiplication

A multiplication algorithm

Answer

Correct Answer: A randomized algorithm for checking the result of a multiplication

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85. What is Cannon's algorithm?

A sorting algorithm

A machine learning algorithm

A pathfinding algorithm

A distributed algorithm, especially suitable for processors laid out in a 2d grid

Answer

Correct Answer: A distributed algorithm, especially suitable for processors laid out in a 2d grid

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86. Which of the following is not an algorithm for matrix multiplication?

Gauss-Seidel algorithm

Winograd's matrix multiplication algorithm

Strassen's matrix multiplication algorithm

Coppersmith-Winograd algorithm

Answer

Correct Answer: Gauss-Seidel algorithm

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87. What is a convergent matrix?

A square matrix whose successive powers approach the zero matrix.

A square matrix whose successive powers approach the identity matrix.

A square matrix whose inverse approaches the zero matrix.

A square matrix whose successive powers diverge.

Answer

Correct Answer: A square matrix whose successive powers approach the zero matrix.

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88. What is an example of a symmetric tridiagonal matrix?

Wilkinson matrix

Toeplitz matrix

Circulant matrix

Hessian matrix

Answer

Correct Answer: Wilkinson matrix

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89. What is an example of a matrix which is extremely ill-conditioned?

Pascal matrix

Toeplitz matrix

Hilbert matrix

Fibonacci matrix

Answer

Correct Answer: Hilbert matrix

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90. What is a Stieltjes matrix?

A symmetric positive definite matrix with positive off-diagonal entries.

A symmetric positive definite matrix with non-zero diagonal entries.

A symmetric positive definite matrix with non-positive off-diagonal entries.

A symmetric positive definite matrix with zero diagonal entries.

Answer

Correct Answer: A symmetric positive definite matrix with non-positive off-diagonal entries.

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91. What is the study of numerical algorithms for linear algebra problems called?

Algebraic linear problems

Numerical linear algebra

Algebraic linear equations

Linear algebra

Answer

Correct Answer: Numerical linear algebra

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92. What is the name of the formula?

Fourier's transform

Exponentiation

Euler's number

Bellard's formula

Answer

Correct Answer: Bellard's formula

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93. What can the Bailey-Borwein-Plouffe formula be used for?

To compute the area of a circle

To compute the volume of a sphere

To compute individual hexadecimal digits of π

To calculate the circumference of a circle

Answer

Correct Answer: To compute individual hexadecimal digits of π

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94. What does the Chudnovsky algorithm do?

Calculates a hypergeometric series

Generates prime numbers

Factorizes a number

Solves quadratic equations

Answer

Correct Answer: Calculates a hypergeometric series

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95. What does Borwein's algorithm do?

It converges exponentially to 1/π

It converges to 1/e

It converges linearly to 1/π

It converges quartically to 1/π

Answer

Correct Answer: It converges quartically to 1/π

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96. What does the Gauss– Legendre algorithm do?

Converges quadratically to π

Find the surface area of a sphere

Find the area of a circle

Find the volume of a cylinder

Answer

Correct Answer: Converges quadratically to π

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97. Which of the following is not a property of Viète's formula?

Converges faster

Infinite product

More complicated

Converges slower

Answer

Correct Answer: Converges faster

Note: This Question is unanswered, help us to find answer for this one

98. What is the Wallis product?

The area of a square

A type of pi

Infinite product converging slowly to π/2

A method of slow converging

Answer

Correct Answer: Infinite product converging slowly to π/2

Note: This Question is unanswered, help us to find answer for this one

99. What is the Leibniz formula for π?

Geometric series with very slow convergence

Alternating series with very slow convergence

Telescoping series with very slow convergence

Arithmetic series with very slow convergence

Answer

Correct Answer: Alternating series with very slow convergence

Note: This Question is unanswered, help us to find answer for this one

100. Who created the first algorithm to compute π to arbitrary precision?

Liu Hui

Johannes Kepler

Gottfried Wilhelm Leibniz

Isaac Newton

Answer

Correct Answer: Liu Hui

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101. What does spigot algorithm refer to?

Algorithms that can find the roots of a polynomial equation

Algorithms that can sort a list of numbers

Algorithms that can compute individual digits of a real number

Algorithms that can find the shortest path between two nodes in a graph

Answer

Correct Answer: Algorithms that can compute individual digits of a real number

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102. What are Gal's accurate tables?

Tables of function values with equal spacing to increase round-off error

Tables of function values with unequal spacing to reduce round-off error

Tables of function values with equal spacing to reduce round-off error

Tables of function values with unequal spacing to increase round-off error

Answer

Correct Answer: Tables of function values with unequal spacing to reduce round-off error

Note: This Question is unanswered, help us to find answer for this one

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