Question: Consider the linear system Ax = e1 based on the 10 Ã 10 pentadiagonal matrix (a) For what values of z are the Jacobi and

Consider the linear system Ax = e1 based on the 10 Ã— 10 pentadiagonal matrix

(a) For what values of z are the Jacobi and Gauss- Seidel methods guaranteed to converge?
(b) Set z = 4. How many iterations are required to approximate the solution to 3 decimal places?
(c) How small can |z| be before the methods diverge?

011z 011 11

Step by Step Solution

★★★★★

3.51 Rating (148 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Diagonal dominance requires z 4 b The solution is u 0115385 0294314 0755853 0536789 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

952-M-L-A-E (3005).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Consider the linear system Ax = b, where A is invertible. Suppose an error b changes b to b' = b + b. Let x' be the solution to the new system; that is, Ax' = b'. Let x' = x + x so that x represents...

Consider the linear system A x = b, where (a) First, solve the equation directly by Gaussian Elimination. (b) Using the initial approximation x(0) = 0, carry out three iterations of the Jacobi...

Consider the linear system Au = b, where (a) What is the solution? (b) Discuss the convergence of the Jacobi iteration method. (c) Discuss the convergence of the Gauss-Seidel iteration method. (d)...

Q3.1 Basic iterative methods 8 Points Consider the iterative solution of a linear system Ax = b of size n x n by iterative method based on a splitting of the matrix A = D + E and the iteration: Xk+1...

Advanced Linear Algebra / Advanced Math / Matlab question need help! Some of the needed codes are attached. In the question, it talks about the HW 6.1 but it can be neglected because every thing...

Math 400 Assignment #3 -- Numerical Integration and Differentiation 1. For the function g x e x 2 2 Due: 6am April 09, 2016 use the centered difference formula with h 101 , 102 , , 1020 to create a...

Solve using Matlab and please solve both problems and all steps Learn how to solve linear systems using the following methods: o MATLAB left division (Gauss elimination) o LU Factorization o...

Ryan Ren Assignment Homework 2 due 09/14/2017 at 02:15pm PDT 1. (1 pt) Compute the following product. \u0014 \u0015\u0014 \u0015 \u0014 5 0 4 7 4 = 0 7 1 7 7 Math4A-02-M17-Wen \u0015 Answer(s)...

Company Law Questions Question 1 Esanda Finance v Peat Marwick (1997) 188 CLR 241 and Daniels v Anderson (1995) 16 ACSR 607 are important decisions regarding auditor's liability. Explain why....

3. Consider the following statement: In data structures, all trees are graphs. State the correctness of the above statement. Making use of suitable diagram(s), justify your answer. (10 marks) 4....

Use the data in anthrop.dat for this problem. 1. Construct a population from the 3000 observations in anthrop.dat in which the 1000 individuals with the highest value of y have been removed. Now take...

2 5 True or False 2 points A reverse mortgage allows you to keep your property while receiving cash from its value. True False

Consider this statement: Banks do not create money because this is the Feds responsibility. Do you agree or disagree? Explain.

The graph of the derivative f of a function f is shown. (a) On what intervals is f increasing or decreasing? (b) At what values of x does have a local maximum or minimum? 6. 5. y= f'(x) y=f'(x) 6. 6.

The graph of the second derivative f of a function f is shown. State the -coordinates of the inflection points of f. Give reasons for your answers. y. -) 8

The graph of the first derivative f of a function f is shown (a) On what intervals is f increasing? Explain. (b) At what values of does f have a local maximum or minimum? Explain. (c) On what...

Given the following information, what is the variance of the returns on a portfolio that is invested 40 percent in both Stocks A and B, and 20 percent in Stock C? (probability of state occurring,...

A worker making 20$ per hour decides to take unpaid leave from work to attend a graduation ceremony. Assuming the worker works an 8 hour day has a total tax rate of 70% and receives a 5% contribution...

Huang Industries is considering a proposed project whose estimated NPV is $12 million. This estimate assumes that economic conditions will be "average." However, the CFO realizes that conditions...