MTH603 Quiz 1 Solution and Discussion

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

Extrapolation

In mathematics, extrapolation is a type of estimation, beyond the original observation range, the value of a variable on the basis of its relationship with another …

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

Interpolation

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In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing new data points within the range of a discrete set of known data points.

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

Divided difference

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Divided differences is a recursive division process. The method can be used to calculate the coefficients in the interpolation polynomial in the Newton form.

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Which of the following systems of linear equations has a strictly diagonally dominant coefficient matrix?
−x1+12x2+5x3=8
9x1+5x2−3x3=12
2x1−4x2+7x3=−15

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Eigenvalues of a _________ matrix are all real.

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

Eigenvalues of a _________ matrix are all real.

If each entry of an n×n matrix A is a real number, then the eigenvalues of A are all real numbers. False. In general, a real matrix can have a complex number eigenvalue. In fact, the part (b) gives an example of such a matrix.

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

@zareen said in MTH603 Quiz 1 Solution and Discussion:

Eigenvalues of a _________ matrix are all real.

If each entry of an n×n matrix A is a real number, then the eigenvalues of A are all real numbers. False. In general, a real matrix can have a complex number eigenvalue. In fact, the part (b) gives an example of such a matrix.
symmetric

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The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____ zeros along its main diagonal.
no
atleast one

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____ zeros along its main diagonal.

NO

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Which of the following systems of linear equations has a strictly diagonally dominant coefficient matrix?

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

Which of the following systems of linear equations has a strictly diagonally dominant coefficient matrix?

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Jacobi’s method is highly recommended for ………… matrix to compute all the Eigen values and the corresponding eigenvectors.

Real symmetric
Non real symmetric
real un-symmetric
non of given

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While using the relaxation method for finding the solution of the following system
11x1+x2−x3=8
x1+8x2+5x3=9 with the initial vector (0,0,0), the residuals would be
x1+x2+9x3=7

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How many Eigen values will exist corresponding to the function; Exp(ax) = e^ax, when the matrix operator is of differentiation?

Finite Multiple
Infinite many
Unique
None

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The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its ________.

The Jacobi method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal (Bronshtein and Semendyayev 1997, p. 892). Each diagonal element is solved for, and an approximate value plugged in. The process is then iterated until it converges.

dy/dx - = 1 - y,y(0) = 0 is an example of

In Double integration, the interval [a, b] should be divided into [c, d) should be divided into --sub intervals of size k. --subintervals of size h and the interval

The (n + 1) th difference of a polynomial of degree n is...

Let P be any real number and h be the step size of any interval. Then the relation between h and P for the backward difference is given by

In integrating $\int_{0}^{\frac{2}{2}} \cos x d x$ by dividing the interval into four equal parts, width of the interval should be

In fourth order Runge-Kutta method K 4

In fourth order Runge-Kutta method k2

What is the Process of finding the values outside the interval (Xo,x,) called?

When we apply Simpson's 3/8 rule, the number of intervals n must be

Milne's P-C method is a multi step method where we assume that the solution to the given initial value problem is known at past --equally spaced points.

The truncation error in Adam's predictor formula is ....-times more than that in corrector formula

To apply Simpson's 3/8 rule, the number of intervals be

Which formula is useful in finding the interpolating polynomial?

Rate of change of any quantity with respect to another can be modeled by

Romberg's integration method is ------ than Trapezoidal and Simpson's rule.

In integrating f, e2* dx by dividing into eight equal parts, width of the interval should be......

To apply Simpson's 1/3 rule, valid number of intervals are?

Newton's divided difference interpolation formula is used when the values of the independent variable are

If there are (n+1) values of y corresponding to (n+1) values of x, then we can represent the function f(x) by a polynomial of degree

MTH603 Assignment 1 Solution and Discussion

MTH603 Quiz 1 Solution and Discussion

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