Dear all,
I am interested in computations with higher precision. The application
is mainly error analysis of high order Magnus integrators. In some cases
the asymptotic behavior of the error can only be observed when the error
is already on double precision and round-off errors of the subroutines
can matter. Computation with higher precision then helps to compute a
reference solution.
Using PETSc/SLEPc with the float128 setting works for me, but I do have
some questions on how it works with Lapack/Blas.
Does PETSc use the standard Lapack package with double precision changed
to quadruple precision?
I did not find a lot about using the standard Lapack with quadruple
precision online, I just saw that all the routines in Lapack expect
double precision input (according to netlib.org).
For example the Lapack routine dstevr for the eigenvalue computation of
small problems which appears in the Lanczos code of SLEPc.
I assume some Lapack methods use parameters which are adjusted on double
precision?
To give an example what kind of parameters would need to be considered:
Using the Matrix Function structure of SLEPc to compute the Matrix
Exponential Function with Krylov methods seems to use a Padé
approximation for the small problem. The used Padé approximation is of
order 6 with scaling and squaring s.t. |H 2^(-s)|<0.5. This choice of
parameter leads to an error smaller than 1e-16 (N. Higham book on Matrix
Functions) for approximating the Matrix Exponential of the small
problem. The solution is then correct only up to double precision even
if higher precision is used for the computations.
My question is how PETSc and SLEPc handle the Lapack methods which are
needed on quadruple precision. My main concern is that some Lapack
methods use parameters which are chosen so that the results are correct
up to double precision.
Thanks for your efforts and greetings,
Tobias Jawecki
