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.

20x₁ + x₂ - x₃ = 17
x₁ - 10x₂ + x₃ = 13
-x₁ + x₂ + 10x₃ = 18

Step by Step Solution

★★★★★

3.34 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The GaussSeidel method takes 4 ... 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_606b0df15d087_695179.pdf

180 KBs PDF File

1623_606b0df15d087_695179.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....

Repeat Exercise 5 using the method of False Position. a. x3 2x2 5 = 0, [1, 4] b. x3 + 3x2 1 = 0, [3,2] c. x cos x = 0, [0, /2] d. x 0.8 0.2 sin x = 0,

Repeat Exercise 1 using Algorithm 6.2. In Exercise 1 a. x1 5x2 + x3 = 7, 10x1 + 20x3 = 6, 5x1 x3 = 4 b. x1 + x2 x3 = 1, x1 + x2 + 4x3 = 2, 2x1 x2 + 2x3 = 3 c. 2x1 3x2 + 2x3 = 5, 4x1 + 2x2 6x3 =...

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 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...

Apply Jacobi's or 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...

On January 1, 2017, Susann, Inc., declared a 15% stock dividend on its common stock when the market value of the common stock was $20 per share. Shareholders' equity before the stock dividend was...

Following several months of online sales and development of new products and materials, you and 5 of your friends decided to take the next step and formalize the existence of your operations, your...

Stocky has a beta of 1 . 2 stop B beta is 1 . 4 6 in stock beta is . 7 2 if you invest $ 2 0 0 0 in its stock $ 3 0 0 0 in stock and $ 5 0 0 0 in stock what will be the pay of your portfolio option 1...

1. Endorphins are a class of morphine-like substances in the brain that are associated with p reduction.

Define linear transformations S: R2 M22 and T: R2 R2 by Compute Can you compute If so, compute it. at b 2c C 2c d ab and T

Define linear transformations S: P1 P2 and T: P2 P1 by S(a + bx) = a + (a + b )x + 2bx2 and T(a + bx + cx2) = b + 2cx Compute (S T) (3 + 2x - x2) and (S T) (a + bx + cx2). Can you compute (T S)...

Define linear transformations S: Pn Pn and T: Pn Pn by S(p (x)) = p(x + 1) and T(p(x)) = p'(x) Find (S T) (p (x)) and (T S) (p (x)).

Diana has regularly contacted three companies (A, B and C) for her quarterly servicing of aircons. If A services her aircons, the probability that there will be no problem with the aircons in the...

GlobalBankCrdit Financial Holdings PLC has the following assets on its balance sheet: Asset Amount Cash and equivalents $5,000,000 Government securities $1,500,000,000 Interbank loans $100,000,000...

Which of the following statements is CORRECT? 1. A time line is not meaningful unless all cash flows occur annually. 2. Time lines are not useful for visualizing complex problems prior to doing...