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Problem 1: Given f(x)= x-4x-5. Solve the following based on fixed point iteration (x=g(x)): 1) the fixed point for the negative root square g(x) function is: 2) the fixed point for the positive root square g(x) function is: 3) Does the negative root square converge to a fixed point? If yes, what's the type of convergence? 4) Does the negative root square converge to a fixed point? If yes, what's the type of convergence?

Problem 1: Given f(x)= x-4x-5. Solve the following based on fixed point iteration (x=g(x)): 1) the fixed point for the negative root square g(x) function is: 2) the fixed point for the positive root square g(x) function is: 3) Does the negative root square converge to a fixed point? If yes, what's the type of convergence? 4) Does the negative root square converge to a fixed point? If yes, what's the type of convergence?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Problem 1: Given f(x)= x²-4x - 5. Solve the following based on fixed point iteration (x=g(x)): 1) the fixed point for the negative root square g(x) function is: 2) the fixed point for the positive root square g(x) function is: 3) Does the negative root square converge to a fixed point? If yes, what's the type of convergence? 4) Does the negative root square converge to a fixed point? If yes, what's the type of convergence? Problem 2: Use the following set of equations to solve points (5, 6, 7, 8, 9, 10, and 11). X1 + 2x2 + X3 = 1 -x1 + x2 + 3x3 = 1 2x1 + x2 + 4x3 = 2 (1) (2) (3) (5) Using Gauss elimination technique, the value of row 3 (R3) in the augmented matrix (A| b) after zeroing elements (a21, a31) is: [ , (6) Using Gauss elimination technique, the value of column 4 (C4) in the augmented matrix (A| b) after zeroing the element (a32) is: [ (7) The exact values of x, and x3 respectively are: [ ] (8) The number of essential row exchanges is: [ (9) U (A) is: (10) -2*|(A)|: [ 11) According to LU decomposition, the Lower matrix (L(A)) is:
Transcribed Image Text:Problem 1: Given f(x)= x²-4x - 5. Solve the following based on fixed point iteration (x=g(x)): 1) the fixed point for the negative root square g(x) function is: 2) the fixed point for the positive root square g(x) function is: 3) Does the negative root square converge to a fixed point? If yes, what's the type of convergence? 4) Does the negative root square converge to a fixed point? If yes, what's the type of convergence? Problem 2: Use the following set of equations to solve points (5, 6, 7, 8, 9, 10, and 11). X1 + 2x2 + X3 = 1 -x1 + x2 + 3x3 = 1 2x1 + x2 + 4x3 = 2 (1) (2) (3) (5) Using Gauss elimination technique, the value of row 3 (R3) in the augmented matrix (A| b) after zeroing elements (a21, a31) is: [ , (6) Using Gauss elimination technique, the value of column 4 (C4) in the augmented matrix (A| b) after zeroing the element (a32) is: [ (7) The exact values of x, and x3 respectively are: [ ] (8) The number of essential row exchanges is: [ (9) U (A) is: (10) -2*|(A)|: [ 11) According to LU decomposition, the Lower matrix (L(A)) is:
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