Write a function in Matlab that takes as input a size n and a tridiagonal matrix

Question

Write a function in Matlab that takes as input a size n and a tridiagonal matrix given as three vectors: n × 1 vector v representing the main diagonal, (n 1) × 1 vector w representing the upper diagonal, and (n 1) × 1 vector z representing the lower diagonal. Have this function output the LU factorization with the U as two vectors and the L as one vector representing the diagonals. Also output the number of flops used. Use only basic programming.

(a) Write out or print out your function.

(b) Run the case with n = 10, v the vector of 2’s, w and z the vector of 1’s, and b the vector of 1’s. Write down your results for the diagonals of L and U.

(c) Run the case with n = 50 and n = 100 with v the vector of 2’s, w and z the vector of 1’s. Write down your results for the number of flops used

Explanation / Answer

n=input('matrix size:');

%random tridiagonal

w=rand(n-1,1);

v=rand(n,1);

z=rand(n-1,1);

%LU decomposition

[w,v,z]=decomt(w,v,z);

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