MATH-6330 - Numerical Methods oed answer key
Showing 181 to 200 of 256 total answers.
#MATH-6330
Awesome StudentQuestion • Numerical Methods
Gauss-Jordan method consists of guessing a value and then using a systematic method to obtain a refined estimate of the root.
Answer
True
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Awesome StudentQuestion • Numerical Methods
The Secant method is convergent for the function f(x) = 3x4 – x -3 whose initial values are present between x0 = 2 and x1 = 4
Answer
True
#MATH-6330
Awesome StudentQuestion • Numerical Methods
Another condition that must be satisfied is that the diagonal elements are all nonzero for the Gauss-Seidel method to be used:
Answer
True
#MATH-6330
Awesome StudentQuestion • Numerical Methods
It is an extension of the Trapezoidal rule This time, it uses three points that would touch the curve of the original function
Answer
Simpson's 1/3 rule
#MATH-6330
Awesome StudentQuestion • Numerical Methods
The relative error is related to the approximate value rather than to the exact value because the true value may not be known.
Answer
True
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Awesome StudentQuestion • Numerical Methods
The Secant method is convergent for the function f(x) = 3x4 – x -3 whose initial values are present between x0 = 0 and x1 = -1
#MATH-6330
Awesome StudentQuestion • Numerical Methods
Using Secant method, what is the value of the next approximated root x2 if x0 = -3 and x1 = 1 for the function f(x) = x3+ 4x+8
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Awesome StudentQuestion • Numerical Methods
In differentiation using numerical methods, one of the steps is interpolating the function by a polynomial p at suitable points
#MATH-6330
Awesome StudentQuestion • Numerical Methods
Using Lagrange interpolation, with data given below compute for f(15)x0 = 0 f(x0) = 2x1 = 3 f(x1) = 7the solution is f(15) = 45
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Awesome StudentQuestion • Numerical Methods
In general, an n =C3=97 n matrix will have a characteristic polynomial of degree of n+ 1, and its roots are the eigenvalues of A
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Awesome StudentQuestion • Numerical Methods
In mathematical modeling, a physical system is translated into mathematical expressions in order to be implemented in computers.
#MATH-6330
Awesome StudentQuestion • Numerical Methods
The relative error is ______________ when the exact value is given by e = 2.718281828 and the approximate value is e a = 2.701.
#MATH-6330
Awesome StudentQuestion • Numerical Methods
Triangular matrices have their eigenvalues on the diagonal of the matrix therefore the eigenvalues of A are the diagonal elements.
#MATH-6330
Awesome StudentQuestion • Numerical Methods
Using the Maclaurin series expansion of cos(x) , when x = will give an approximate value of 0.6073 using the first two terms only.
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Awesome StudentQuestion • Numerical Methods
In Newton-Cotes integration methods, the nodes are uniformly distributed in [a, b] with x0 = a, xn = band the spacing h = (b - a) / n
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Awesome StudentQuestion • Numerical Methods
Approximating calculations which involve infinite value, most often used in series notations and in calculus doesn't introduce errors.
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Awesome StudentQuestion • Numerical Methods
In the factorization A = LU the matrix L is lower triangular and the matrix U is upper triangular, it is called Crout factorization when
#MATH-6330
Awesome StudentQuestion • Numerical Methods
The secant method can fail to find a root of a nonlinear function that has a small slope near the root assures the presence of the root.
#MATH-6330
Awesome StudentQuestion • Numerical Methods