NEPNLEIGSSetSingularitiesFunction#

Sets a user-defined callback function to compute a discretization of the singularity set (the values where \(T(\cdot)\) is not analytic).

Synopsis#

#include "slepcnep.h" 
PetscErrorCode NEPNLEIGSSetSingularitiesFunction(NEP nep,NEPNLEIGSSingularitiesFn *fun,void *ctx)

Logically Collective

Input Parameters#

nep - the nonlinear eigensolver context
fun - user function (if NULL then NEP retains any previously set value)
ctx - [optional] user-defined context for private data for the function (may be NULL, in which case NEP retains any previously set value)

Notes#

If the problem type has been set to NEP_RATIONAL with NEPSetProblemType(), then it is not necessary to set the singularities explicitly since the solver will try to determine them automatically.

If the problem is NEP_GENERAL, it is also possible to omit the singularities callback. In that case, a discretization of the singularity set is approximated via the AAA algorithm [Elsworth and Güttel, 2019, Nakatsukasa et al., 2018].

References#

[Els19]

S. Elsworth and S. Güttel. Conversions between barycentric, RKFUN, and Newton representations of rational interpolants. Linear Algebra Appl., 576:246–257, 2019. doi:10.1016/j.laa.2018.10.003.

[Nak18]

Y. Nakatsukasa, O. Sète, and L. N. Trefethen. The AAA algorithm for rational approximation. SIAM J. Sci. Comput., 40(3):A1494–A1522, 2018. doi:10.1137/16m1106122.