### DPOTRS in extended precision?

Posted:

**Thu Jun 20, 2019 5:35 pm**Hello:

I must deal with a symmetric system of equations, A*x=B with a very badly conditioned matrix (cond ~ 1.0e21). Solving the problem with double precision routines (using GNU Octave, which calls Lapack) I obtain a solution, but as the forward error bound (if I remember correctly) is FE<=cond(A)*epsilon, and epsilon is 2.22e-16, the forward error is bounded by the number 2e5, which I find so big.

Then, I would like to check the solution of the problem using quadruple precision (128 bits), as the corresponding machine epsilon is ~2e-34. I know there is the XBLAS implementation of BLAS in extended precision, but what about Lapack? Is there a Lapack implementation in extended precision? I would like to use the DPOTRS subroutine in extended precision in order to solve my problem. Is it possible?

Thanks

I must deal with a symmetric system of equations, A*x=B with a very badly conditioned matrix (cond ~ 1.0e21). Solving the problem with double precision routines (using GNU Octave, which calls Lapack) I obtain a solution, but as the forward error bound (if I remember correctly) is FE<=cond(A)*epsilon, and epsilon is 2.22e-16, the forward error is bounded by the number 2e5, which I find so big.

Then, I would like to check the solution of the problem using quadruple precision (128 bits), as the corresponding machine epsilon is ~2e-34. I know there is the XBLAS implementation of BLAS in extended precision, but what about Lapack? Is there a Lapack implementation in extended precision? I would like to use the DPOTRS subroutine in extended precision in order to solve my problem. Is it possible?

Thanks