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Consider the system of linear equations :) -- ( ;) 3 1 8 5 In the following, let A denote the coefficient matrix in (1). a) Compute the 1-norm of the matrix A. |A|1 = b) Compute the condition number cond, (A) of the matrix A. cond, (A) = c) Perform the first two steps of the Jacobi method for the starting vector æ0) - (0, 0)". a1) = ( a(2) = ( %3D d) is the general criterion far convergence of the Jacobi method (as introduced in the lecture) satisfied in this case? e) Compute the exact solution a of the system of equations (1).

Consider the system of linear equations :) -- ( ;) 3 1 8 5 In the following, let A denote the coefficient matrix in (1). a) Compute the 1-norm of the matrix A. |A|1 = b) Compute the condition number cond, (A) of the matrix A. cond, (A) = c) Perform the first two steps of the Jacobi method for the starting vector æ0) - (0, 0)". a1) = ( a(2) = ( %3D d) is the general criterion far convergence of the Jacobi method (as introduced in the lecture) satisfied in this case? e) Compute the exact solution a of the system of equations (1).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 23EQ
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Consider the system of linear equations (: :) --(;) 3 1 8 5 In the following, let A denote the coefficient matrix in (1). a) Compute the 1-norm of the matrix A. ||4|| = b) Compute the condition number cond, (A) of the matrix A. cond, (A) = c) Perform the first two steps of the Jacobi method for the starting vector æ) – (0, 0)". a1) = ( 2(2) %3D d) Is the general criterion far convergence of the Jacobi method (as introduced in the lecture) satisfied in this case? e) Compute the exact solution a of the system of equations (1).
Transcribed Image Text:Consider the system of linear equations (: :) --(;) 3 1 8 5 In the following, let A denote the coefficient matrix in (1). a) Compute the 1-norm of the matrix A. ||4|| = b) Compute the condition number cond, (A) of the matrix A. cond, (A) = c) Perform the first two steps of the Jacobi method for the starting vector æ) – (0, 0)". a1) = ( 2(2) %3D d) Is the general criterion far convergence of the Jacobi method (as introduced in the lecture) satisfied in this case? e) Compute the exact solution a of the system of equations (1).
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