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Numerical Methods

Showing 1-75 of 256 answers

=E2=88=8F is a symbol used in Lagrange Interpolating polynomial which designates
  • pi
  • =E2=80=9Cthe inverse of=E2=80=9D
  • =E2=80=9Ca product of=E2=80=9D Correct
  • =E2=80=9Cthe sum of=E2=80=9D
A column vector is denoted by a boldface lowercase letter and expressed as
  • 1 x n matrix
  • n x 1 matrix Correct
  • no correct answer
  • m x n matrix
A continuous function's integral is approximated using either the trapezoidal or Simpson's rule by translating the function into discrete form
  • True Correct
  • False
A cubic polynomial can interpolate three points
  • True
  • False Correct
A diagonal matrix could be an identity matrix if the diagonals have a value of
  • any non-zero
  • 1 Correct
  • no correct answer
  • 0
A Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose and can be decomposed using Cholesky’s method.
  • True Correct
  • False
A mathematical model that will compute the following limit as  will readily give _____________ answer.
  • 0
  • infinite
  • indeterminate Correct
  • finite
A matrix decomposition method that has an upper triangular matrix and an orthogonal matrix is referred to as the QR 
  • True Correct
  • False
A matrix is symmetric/ Hermitian positive definite matrix if
  • No correct answer
  • the resulting triangular factors are equal to each other
  • the resulting triangular factors are the negative value of each other
  • the resulting triangular factors are the transpose of each other Correct
A matrix which is denoted by a boldface lowercase letter and expressed as 1 x n matrix is
  • no correct answer
  • column vector Correct
  • row vector
  • not a matrix
A root finding method also known as the Tangent method is
  • Newton's method Correct
  • Open method
  • Secant Method
  • Bisection method
A root finding method which requires the function to be differentiable
  • Newton-Raphson iteration Correct
  • Bisection
  • False position
  • Secant Method
A row vector is denoted by a boldface lowercase letter and expressed as a
  • 1 x n matrix Correct
  • m x n matrix
  • n x 1 matrix
  • no correct answer
A square matrix is said to be diagonally dominant if for every row of the matrix, the magnitude of the diagonal entry in a row is less than or equal to the sum of the magnitudes of all the other (non-diagonal) entries in that row.
  • True Correct
  • False
Algorithms should have explicitly defined set of inputs and outputs
  • True Correct
  • False
Also called trapezoidal rule It approximates the area under a curve by atrapezoidwith horizontal base and sloped top (connecting the endpointsx1andx2)
  • 2-point closed Newton-Cotes formula Correct
  • Newton-Raphson
  • Gauss-Seidel
  • Gauss-Jordan
Among the many applications of matrices are used in statistics, economics, physics, and engineering.
  • True Correct
  • False
An additional benefit of the power method is that the corresponding eigenvector is obtained as a by-product of the method.
  • True Correct
  • False
An algorithm design technique is a general approach to solving problems algorithmically that is applicable to a variety of problems from different areas of computing
  • True Correct
  • False
An integral expressed as the difference between the values of the integral at specified upper and lower limits of the independent variable
  • indefinite integral
  • improper integral
  • proper integral
  • definite integral Correct
Another condition that must be satisfied is that the diagonal elements are all nonzero for the Gauss-Seidel method to be used:
  • True Correct
  • False
Another method called midpoint rule is an open type method numerical integration
  • True Correct
  • False
Approximating calculations which involve infinite value, most often used in series notations and in calculus doesn't introduce errors.
  • True
  • False Correct
Best-case is the maximum number of steps taken on any instance of size of a variable
  • True
  • False Correct
By applying the power method to the matrix inverse of [A], the power method will ________on the largest value of 1/λ in other words, the smallest value of λ
  • no correct answer
  • diverge
  • converge Correct
  • fail
Cholesky’s Method is based on the fact that a symmetric matrix can be decomposed into triangular factors are the transpose of each other.
  • True Correct
  • False
Choosing an initial guess which gives near f(x) = 0 is considered a good guess
  • True Correct
  • False
Compute for the determinant of the 2 x 2 matrix defined as
  • D = 125
  • D = 0875 Correct
  • No correct answer
  • D = - 0675
Creating a mathematical model that will compute the following limit as  will produce a result of
  • 0
  • 1 Correct
  • indeterminate
  • infinite
Direct method for finding the eigenvalues is recommended since the calculation of zeros of a polynomial is numerically challenging if not unstable.
  • True Correct
  • False
Each component of the new iterates in Gauss-Seidel method depends upon all previously computed components, the updates cannot be done simultaneously.
  • True Correct
  • False
Eigenvalues are used in the analysis of linear transformation such as scaling.
  • True Correct
  • False
Find the missing value to satisfy that y = 1/24x +2y +2z = 8x + 4y - 2z = ?3x +y - z = 4
  • 4
  • 05
  • 3
  • 2 Correct
First order differences is equivalent f[x0,x1] when i = 0
  • True Correct
  • False
For  is the iteration may terminate if the difference between f (x)  is already zero.
  • True Correct
  • False
For a two segment trapezoidal rule, it will use the points similar to the ones used by Simpson's 1/3 rule
  • True Correct
  • False
For an interval of 0 to 1, a subinterval with a size of 02 will give n = 5 described as 5 segment Trapezoidal rule
  • True Correct
  • False
For both the Trapezoidal and Simpson's 1/3 rule , using more strips will give better approximation of the curve
  • True Correct
  • False
For practical reasons, the absolute error is usually more meaningful than the relative error.
  • True
  • False Correct
For the function  , its first derivative is  f’(x) is  
  • True Correct
  • False
For the function  f(x) =its first derivative is  f’(x) is   The first derivative of the function   is f’(x) = 
  • True Correct
  • False
For the function f(x) = ex-2 the next approximated value of the root when x0 = -1 and x1 = 1 is x2 =  0.98626.
  • True Correct
  • False
For the function f(x) = ex-2 the value of f(x2) when x0 = -1 and x1 = 1 is f(x) =  -0.5248
  • True Correct
  • False
For the given systems of linear equations, with initial values x1 =0;  x2 =0; x3 = 0. The next iterative value of x1 using Gauss-Seidel Method is 1.3333.
  • True Correct
  • False
For the given systems of linear equations, with initial values x1 =0;  x2 =0; x3 = 0. The next iterative value of x2 using Gauss-Seidel Method is 1.5. 
  • True Correct
  • False
For the given systems of linear equations, with initial values x1 =0;  x2 =0; x3 = 0. The next iterative value of x3 using Gauss-Seidel Method is 0.5278. 
  • True Correct
  • False
From the two data points (1,4) and (3, 7), and (4,10) using Lagrange polynomial method, the polynomial is Li(x) = 05x2-05x +2
  • True
  • False Correct
From the two data points(2,5) and (6, 11), using Lagrange polynomial method, the polynomial is Li(x) = 15x +2
  • True Correct
  • False
Gauss-Jordan method consists of guessing a value and then using a systematic method to obtain a refined estimate of the root.
  • True Correct
  • False
Gaussian elimination has no specific row operations Various ways can be employed but may come up with the same answer
  • True Correct
  • False
Given a matrix A , its QR -decomposition is an upper triangular matrix and an orthogonal matrix. An orthogonal matrix is a matrix whose transpose is equivalent to its inverse.
  • True Correct
  • False
Given the function f(x) = 075 + 11x, an exact value can be given instantly by Trapezoidal rule
  • True Correct
  • False
Horner’s method which is a method for finding roots of a polynomial equation f(x) =0 is almost similar to Newton’s method.
  • True Correct
  • False
How much error would be observed for the integral of f(x) = sin2x + 5 for an interval of [0,1] if n = 1 or if n = 2?
  • approximately 05
  • approximately 1
  • greater than 1
  • almost negligible Correct
If A is a 3 x 3  matrix and B is a 3x2 matrix , the statement “ A – B is not possible” is
  • True Correct
  • False
If a matrix has its entire diagonal elements are positive, then the real parts of its eigenvalues are negative.
  • True Correct
  • False
If A−1 (if it exists) the eigenvalues of A−1 is 1/5, 1/4 and 1/2 if matrix A has eigenvalues 5, 4 and 2
  • True Correct
  • False
If A−1 (if it exists) the eigenvalues of A−1 is 1/5, ¼ and ½ if matrix A  has eigenvalues 5, 4 and 2.
  • True Correct
  • False
If matrix A gives the largest eigenvalue, it suggests that if A -1 exists, the smallest eigenvalue can be obtained through inverse power method.
  • True Correct
  • False
If matrix A is invertible such that A−1 = L−TL−1 then matrix A can be decomposed using Cholesky’s method.
  • True Correct
  • False
If matrix is A is positive definite then a11 > 0. 
  • True Correct
  • False
If QT is the transpose of Q then QT Q = I or the identity matrix.
  • True Correct
  • False
If the determinant of the matrix is zero, it is impossible to check the solutions of the variables using
  • Gaussian Elimination method
  • Neither "Cramer's Rule" nor "Gaussian Elimination method" is correct
  • Cramer's Rule Correct
  • Both "Cramer's Rule" and "Gaussian Elimination method" are correct
If the eigenvalues are repeated roots λ1 = λ2 = λ3, then the characteristic polynomial is of
  • 2nd degree polynomial
  • 3rd degree polynomial Correct
  • is an n-1 polynomial
  • no correct answer
If the function, f(x) = cos3x was approximated by the polynomial, P(15) = -02, the amount of error approximately 005
  • True Correct
  • False
If the interval of the function is given as 0 to pi, for n = 6 segments, each node or segments will be
  • True Correct
  • False
If the magnitude of the diagonals is greater than the sum of the non-diagonals in the same row, then the matrix is not diagonally dominant.
  • True Correct
  • False
If the main determinant is zero the system of linear equations is
  • Both "inconsistent" and "has infinite many solutions" are correct Correct
  • Has infinite many solutions
  • Inconsistent
  • Neither "inconsistent" nor "has infinite many solutions" is correct
If the number of segments, n= 20 Compute for the stepsize, h if the interval is from 0 to 1
  • h = 05
  • h = 005 Correct
  • h = 020
  • h = 002
If the tridiagonal coefficient matrix is diagonally dominant, then procedure Tri
  • no correct answer
  • will diverge
  • will encounter zero divisors Correct
  • will not encounter zero divisors
If there is a randomized algorithm that solves a decision problem in time t and outputs the correct answer with probability 05, then there is a randomized algorithm for the problem that runs in time =CE=98(t) and outputs the correct answer with probability at least 099
  • True
  • False Correct
If x2 is the approximated root in Secant method, it follows that; the value of f(x2) must be equal to 0.
  • True Correct
  • False
If you need to evaluate a definite integral involving a function whose anti derivative cannot be found, it is easier to resort to this approximation technique
  • Direct Method
  • Cholesky's Method
  • Power Method
  • Trapezoidal method Correct
In creating a computer algorithm one important factor that should be considered is that the user would be prompted the values that are needed in solving.
  • True Correct
  • False
In differentiation using numerical methods, one of the steps is interpolating the function by a polynomial p at suitable points
  • True Correct
  • False
This course is taught by the mentor:
Professor Franzelino Abella

Franzelino Abella

Master of Arts in Mathematics Education specialization in College Teaching.

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