'Nep2rat' is a tool to rationally approximate nonlinear matrix-valued functions, mainly aimed to solve nonlinear eigenvalue problems.
This repository contains the function "nep2rat" which approximates the nonlinear functions, and all the experiments proposed in the referenced paper. Those experiments require the installation of the NLEVP library.
[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.
Güttel, S., Negri Porzio, G.M. and Tisseur, F., 2020. Robust rational approximations of nonlinear eigenvalue problems. MIMS Eprints 2020.24