topic Bad Conditioned Linear System in Intel® oneAPI Math Kernel Library

Bad Conditioned Linear System

Gianluca_G_1 — Thu, 04 May 2017 07:33:36 GMT

The problem is to calculate the array of functions f(x) defined as:

see Figure1

and then

see Figure2

Some coefficients of the matrix “A” are in the form:

see Figure3

For this reason, for large values “x” the matrix “A” becomes singular and the linear system bad conditioned.

Anyway, in double precision if “x > 706” the calculation of the coefficient gives underflow.

Matrix preconditioning seems not effective.

Are there math trick to overcome the problem?

Hi Gianluca,

Ramon_A_ — Mon, 08 May 2017 07:35:26 GMT

Hi Gianluca,

Have you tried to obtain the LU decomposition and next use solve_triangular?

You can either do it manually with scipy.linalg.lu and scipy.linalg.solve_triangular or use the function dgesv. The first option will allow you to control better the middle steps, the second option is more confortable.

Note that if the matrix is defined positive, you can use the cholesky factorization instead of the LU.

At the end, we have solved

Gianluca_G_1 — Mon, 08 May 2017 11:11:23 GMT

At the end, we have solved the problem preconditioning the linear system coefficient matrix.

Thank you very much

Gianluca