Nep2rat

Nep2rat is a tool to rationally approximate nonlinear matrix-valued functions, mainly aimed to solve nonlinear eigenvalue problems

[Am, Bm, Rm] = nep2rat(F, Z)

returns the rational approximation Rm of the function F on the target set Z, and the linearized pencil (Am, Bm). The set Z must be given as a vector of points, while F could either be a function_handle or a struct, with fields:

F.coeffs: the matrix coefficients of F;
F.fun: the scalar functions that define f;

This structure mirrors the output of the NLEVP library. The default behaviour changes with the input F: if F is a function_handle, then nep2rat uses the "surrogate AAA with cyclic Leja--Bagby refinement" algorithm, while if F is a struct, it uses the "weighted AAA" algorithm. If the split form of F is available, we suggest to use the struct form of F as the input.

[Am, Bm, Rm, info] = nep2rat(F, Z, opts)

allows the user to specify many optional parameters, such as the precision of the approximation and the algorithms utilised. The output info is returns additional information, while opts is a structure with all the. An in-depth guide is contained in the help of nep2rat.