I want to solve a linear set of equations (
Ax=b) using LU decomposition. My
"A" matrix is a complex matrix which is symmetrical.
The code that I work has two parts. In the first part I do all the initialization where I compute L and U factors of the matrix.
The second part of the code runs in every time-step (which is specified in the beginning). In this section, I solve the equations
Ld=b and Ux=d to find the solution vector
x. And the computer which runs this part has limited memory. Also, I want this part to be as efficient as possible.
So my questions are:
Is there a way to save some memory for storing the L and U matrices of a symmetric complex matrix? If I deal with just an inverse instead of L and U I can just store the half of the matrix. Is there a similar way to save some storage for L and U matrices.
What are the methods that I can use to improve the efficiency of a LU decomposition for a complex symmetric matrix?