A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal and the ones immediately above and below it.Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don't need to be modified or added. As an example, consider a linear system Ax = b with 100,000 unknowns and the same number of equations. The coefficient matrix A is tridiagonal, with all elements on the main diagonal equal to 3 and all elements on the diagonals above and below it equal to 1. The vector of constant terms b contains all ones, except that the first and last elements are zero. You can use td to find that x1= −0.10557.
IN PYTHON
A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal and the ones immediately above and below it.Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don't need to be modified or added. As an example, consider a linear system Ax = b with 100,000 unknowns and the same number of equations. The coefficient matrix A is tridiagonal, with all elements on the main diagonal equal to 3 and all elements on the diagonals above and below it equal to 1. The
The following code format should help:
def td(l, m, u, b):
'''Solve a linear system Ax = b where A is tridiagonal
Inputs: l, lower diagonal of A, n-1 vector
m, main diagonal of A, n vector
u, upper diagonal of A, n-1 vector
b, right-hand constant in each equation, n vector
Output: x, vector of unknowns, n vector
Example: if A = 2 -2 0 0
-1 4 -2 0
0 -1 6 -2
0 0 -1 8
and b = [24; 12; -98; 55],
then l = [-1; -1; -1], m = [2; 4; 6; 8], u = [-2; -2; -2],
and x = [10; -2; -15; 5]'''
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