implement using matlab Purpose: To solve Ax=b, given an initial approximation x(0). INPUT: The number of equations and unknowns n; the matrix (A)ij?=aij?, the entries bi?, the entries of XO=x(0), for 1?i,j?n; the error tolerance TOL; the maximum number of iterations N. OUTPUT: The approximate solution x1?,,xn? or a message that the number of ite solutionspile.com

Question

implement using matlab
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Purpose: To solve

Ax = b

, given an initial approximation

x^{(0)}

. INPUT: The number of equations and unknowns

n

; the matrix

(A)_{ij} = a_{ij}

, the entries

b_{i}

, the entries of

XO = x^{(0)}

, for

1 ? i, j ? n

; the error tolerance

TO L

; the maximum number of iterations

N

. OUTPUT: The approximate solution

x_{1}, \dots, x_{n}

or a message that the number of iterations was exceeded. Step 1. Set

k = 1

Step 2. While

k ? N

do Steps 3-6. Step 3. For

i = 1, \dots, n

Set

x_{i} = (b_{j} ? ?_{j = 1}^{j ? 1} a_{j} x_{j} ? ?_{j = i + 1}^{n} a_{ij} X O_{j}) / a_{ij}

Step 4. If

? x ? XO ? < TO L

, then OUTPUT

x_{1}, \dots, x_{n}

. STOP Step 5. Set

k = k + 1

Step 6. For

i = 1, \dots, n

set

X O_{i} = x_{i}

. Step 7. OUTPUT('Max number of iterations exceeded'). STOP

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