Consider an n by n tridiagonal matrix A where there is 3 on the diagonal and -1 on both sub-and super-diagonal. For eg, when n=4 the matrix will be(adsbygoogle = window.adsbygoogle || []).push({});

[3 -1 0 0]

[-1 3 -1 0]

[0 -1 3 -1]

[0 0 -1 3]

Let b be the vector where bi = 1/i.

(a) For n=4 find the value of T for the Jacobi method and find ||T||∞.

(b) Will the norm be any different for a large value of n? Give a reason for your answer.

(c) For n=25, write a Matlab script file to perform 4 iterations of Jacobi method to estimate the solution of Ax=b. Use the zero vector for your first estimate.

Answer:

(a) T=

[0 0.33 0 0]

[0.33 0 0.33 0]

[0 0.33 0 0.33]

[0 0 0.33 0]

Therefore, ||T||∞ = 2/3

(b) No it will not because the max the row sum will ever be in tridiagonal matrix is 2/3.

Now can anyone help me with part (c) please!!!!!!

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# Need help with 1 part of the question reg Matlab

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