WORK IN PROGRESS
This package solves matrix polynomial equations in the form
A0 + A1*X + A2*X*X = 0
or
- - - -
| I | | I |
D| - | X1 = E| - |
| X2 | | X2 |
- - - -
where matrices X1 and X2 contain columns from the solution matrix
X.
Two algorithms are provided
Cyclic reduction
cyclic_reduction!(x::Array{Float64},a0::Array{Float64},a1::Array{Float64},a2::Array{Float64},ws::CyclicReductionWs, cvg_tol::Float64, max_it::Int64)
Solve the quadratic matrix equation a0 + a1x + a2x*x = 0, using the cyclic reduction method from Bini et al. (???).
The solution is returned in matrix x. In case of nonconvergency, x is set to NaN and
UndeterminateSystemExcpetion or UnstableSystemException is thrown
Example
using CyclicReduction
n = 3
ws = CyclicReductionWs(n)
a0 = [0.5 0 0; 0 0.5 0; 0 0 0];
a1 = eye(n)
a2 = [0 0 0; 0 0 0; 0 0 0.8]
x = zeros(n,n)
cyclic_reduction!(x,a0,a1,a2,ws,1e-8,50)
## General Schur Decomposition
gs_solver!(ws::GsSolverWs,d::Matrix{Float64},e::Matrix{Float64},n1::Int64,qz_criterium)
The solution is returned in ``ws.g1`` and ``ws.g2``