MTH603 Quiz 1 Solution and Discussion

cyberian

A square matrix is said to be diagonally dominant if the magnitude of the diagonal element in a row is greater than or equal to the sum of the magnitudes of all the other non-diagonal elements in that row for each row of the matrix.

cyberian

Simplifying
0x + 0y = 2

Anything times zero is zero.
0x + 0y = 2

Anything times zero is zero.
0 + 0y = 2

Combine like terms: 0 + 0 = 0
0 = 2

Solving
0 = 2

Couldn’t find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.

cyberian

In numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in.

cyberian

while using relaxation method, which of th folowing is the

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Solution to the linear equation 2x + 0y = 0

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the linear equation 2x-0y-2=0 has

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The primary use of iterative methods is for computing the solution to large, sparse systems and for finding a few eigenvalues of a large sparse matrix. Along with other problems, such systems occur in the numerical solution of partial differential equations.

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A system is inconsistent if it has no solution. In a system of two equations in two variables, the equations are dependent if one equation is a multiple of the other. Dependent systems have an infinite number of solutions – every point is a solution.

cyberian

@cyberian said in MTH603 Quiz 1 Solution and Discussion:

The primary use of iterative methods is for computing the solution to large, sparse systems and for finding a few eigenvalues of a large sparse matrix. Along with other problems, such systems occur in the numerical solution of partial differential equations.

This chapter discusses the use of iterative methods in the solution of partial differential equations. Most of the large sparse systems, which are solved by iterative methods, arise from discretizations of partial differential equations. The value of a particular generality is a function of the problem or class of problems to be solved. Three basic parts of a computer program to solve a boundary-value problem are the mesh generation, the discretization, and the solution of the matrix problem. The mesh generation and the discretization parts determine the accuracy or value of the numerical solution, while the matrix solution part determines most of the computer solution cost. These three parts are not independent of each other. Increased generality in the mesh generation and discretization parts can significantly increase the matrix solution cost. Thus, solution cost can only be given as a function of the mesh decomposition and discretization methods under consideration. The factors that mostly affect matrix solution costs are total arithmetic operations required, storage requirements, and overhead because of data transmission and logical operations associated with the implementation of the solution method. The most efficient solution procedures usually are those that minimize storage and arithmetic requirements.

cyberian

@cyberian said in MTH603 Quiz 1 Solution and Discussion:

A system is inconsistent if it has no solution. In a system of two equations in two variables, the equations are dependent if one equation is a multiple of the other. Dependent systems have an infinite number of solutions – every point is a solution.

Two Variables
In a system of two equations in two variables, the equations are dependent if one equation is a multiple of the other. Dependent systems have an infinite number of solutions – every point is a solution.

cyberian

@cyberian said in MTH603 Quiz 1 Solution and Discussion:

the linear equation 2x-0y-2=0 has

cyberian

@cyberian said in MTH603 Quiz 1 Solution and Discussion:

while using relaxation method, which of th folowing is the

2x+3y = 1, 3x +2y =4 ?
(1,4)

cyberian

In … method, the elements above and below the diagonal are simultaneously made zero.

cyberian

gauss seidel method also known as?

cyberian

@cyberian said in MTH603 Quiz 1 Solution and Discussion:

gauss seidel method also known as?

Gauss–Seidel method is an improved form of Jacobi method, also known as the successive displacement method. This method is named after Carl Friedrich Gauss (Apr.

cyberian

Which of the following rearrangements make the system of linear equations strictly diagonally dominant: 39 + 2 = -2 62 + 4y + 11z = 1 5r - 23 - 22 = 9 Select one: 2v - 22 = 9 3y = 2 6z + 4y + M = 1 6r + 4y + M = 1 -8v + 2 = -2 51 - %0 - 22 = 0 61 - %v - 28 - 0 Av + M2 = 30 + 2 = -2 No need to rearrange as the system is already diagonally dominant.
Which of the following rearrangements make the system of linear equations strictly diagonally dominant:
39 + 2 = -2
62 + 4y + 11z = 1
5r - 23 - 22 = 9

Select one:
2v - 22 = 9
3y = 2
6z + 4y + M = 1
6r + 4y + M = 1
-8v + 2 = -2
51 - %0 - 22 = 0
61 - %v - 28 - 0 Av + M2 = 30 + 2 = -2

No need to rearrange as the system is already diagonally dominant.

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MTH603 Assignment 1 Solution and Discussion

MTH603 Quiz 1 Solution and Discussion

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