MTH603 Quiz 1 Solution and Discussion
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@zareen said in MTH603 Quiz 1 Solution and Discussion:
Interpolation
Reff
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. -
@zareen said in MTH603 Quiz 1 Solution and Discussion:
Divided difference
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 -
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 -
@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 -
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 -
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 -
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.
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The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.
The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric________ definite matrices. Explanation: Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices because only in this case convergence is possible.