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Gianluca_G_1

Beginner

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11-08-2017
08:13 AM

22 Views

Avoid matrix inversion is it always possible?

We need to solve a linear system with a dense matrix of complex numbers.

When the size of the matrix is lower than 4 GB (Microsoft limits for 64 bit systems) we can use MKL routines directly to solve:

Instead when the matrix is bigger than 4 GB we divide the matrix in blocks:

The linear system becomes:

From (1) we obtain:

**Solving equation (6) the solution x2 is obtained.**

**Using x2 in (3) it is easy to calculate x1.**

**This algorithm is interesting but introduces a matrix inversion.**

**This is a big problem when the linear system is ill conditioned.**

**Any suggestion to solve the problem avoiding the matrix inversion?**

Thankyou

Gianluca

1 Reply

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Alexander_K_Intel2

Employee

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11-08-2017
08:19 AM

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Answered on initial thread https://software.intel.com/en-us/forums/intel-math-kernel-library/topic/748079#comment-1914725

Thanks,

Alex

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