Question: Repeat the given exercise using the GaussSeidel method. Take the zero vector as the initial approximation and work with four-significant-digit accuracy until two successive iterates

Repeat the given exercise using the GaussSeidel method. Take the zero vector as the initial approximation and work with four-significant-digit accuracy until two successive iterates agree within 0.001 in each variable. Compare the number of iterations required by the Jacobi and Gauss-Seidel methods to reach such an approximate solution.

3x₁ - x₂ = 1
-x₁ + 3x₂ - x₃ = 0
-x₂ + 3x₃- x₄ = 1

-x₃ + 3x₄ = 1

Step by Step Solution

★★★★★

3.52 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The GaussSeidel method takes 7 steps while the Jacobi ... 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 (2 attachments)

1623_606b0df15d17e_695181.pdf

180 KBs PDF File

1623_606b0df15d17e_695181.docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Repeat Exercise 3 using the Jacobi method. Repeat Exercise Use the QR Algorithm to determine, to within 105, all the eigenvalues for the matrices given in Exercise 1. In exercise a. b. c. d. e. f....

3x1 - x2 + x3 = 4 - x1 + 7x2 - 2x3 = 1 2x1 + 6x2 - x3 = 5 Solve by Cramer's rule, where it applies.

Repeat Exercise 1 using = 1.3. In Exercise 1 a. 3x1 x2 + x3 = 1, 3x1 + 6x2 + 2x3 = 0, 3x1 + 3x2 + 7x3 = 4. b. 10x1 x2 = 9, x1 + 10x2 2x3 = 7, 2x2 + 10x3 = 6. c. 10x1 + 5x2 = 6, 5x1 + 10x2 4x3 =...

Repeat the given exercise using the GaussSeidel method. Take the zero vector as the initial approximation and work with four-significant-digit accuracy until two successive iterates agree within...

Apply the Gauss-Seidel method to the given system. Take the zero vector as the initial approximation and work with four-significant-digit accuracy until two successive iterates agree within 0.001 in...

Apply Jacobis method to the given system. Take the zero vector as the initial approximation and work with four-significant-digit accuracy until two successive iterates agree within 0.001 in each...

In Exercises 1-3, apply Jacobi's method to the given system. Take the zero vector as the initial approximation and work with four-significant-digit accuracy until two successive iterates agree within...

Apply Jacobis method to the given system. Take the zero vector as the initial approximation and work with four-significant-digit accuracy until two successive iterates agree within 0.001 in each...

Apply Jacobi's method to the given system. Take the zero vector as the initial approximation and work with four-significant-digit accuracy until two successive iterates agree within 0.001 in each...

Apply Jacobis method to the given system. Take the zero vector as the initial approximation and work with four-significant-digit accuracy until two successive iterates agree within 0.001 in each...

The cash book of Mr. Mbindawina shows K836,400 as bank balance as at 31 December 2019. However, you discover that it does not agree with the balance as per bank statement. On scrutiny, you find the...

In 2021, Alex had paid $5,000 in qualified tuition and fees. His filing status is Single, and his Adjusted Gross Income is $50,000. How much of a qualified tuition and fees deduction can he take in...

ince many buyers are leery of buying a product advertised on an infomercial, one way marketers can reduce potential customer dissatisfaction about the item is to offer which of the following?...

Let T: V V be a linear transformation such that T T = T. (a) Show that {v, T(v)} is linearly dependent if and only if T(v) = v or T(v) = 0. (b) Give an example of such a linear transformation with...

Prove that S + T and cT are linear transformations. The set of all linear transformations from a vector space V to a vector space W is denoted by (V, W) . If S and T are in (V, W), we can define the...

Prove that (V, W) is a vector space with this addition and scalar multiplication.

As a financial advisor, you are assigned a new client who is considering investing in one of two stocks, A or B. The table below shows information about the performance of stocks A and B last year....

List 2 Big Data products or solutions.

Home work: A report on "Gas Lift". Not less than 500 words.