GeneralizedSylvesterSolver.jl

Author DynareJulia
Popularity
1 Star
Updated Last
10 Months Ago
Started In
January 2022

GeneralizedSylvesterSolver.jl

[WORK IN PROGRESS] This Julia package solves

a x + b x (c ⊗ c ⊗ ... ⊗ c) = d

by using

(I + c^T ⊗ c^T ⊗ ... ⊗ c^T ⊗ b)x = d

Installation

The package requires Julia 1.6.3 or higher

using Pkg
Pkg.add("GeneralizedSylvesterSolver")

Usage

ws = IPlusAtKronBWs(ma, mb, mc, order)
generalized_sylvester_solver!(a::AbstractMatrix, b::AbstractMatrix, c::AbstractMatrix,
                              d::AbstractMatrix, order::Int64, ws::IPlusAtKronBWs)

whith

  • a is a ma x na matrix
  • b is a mb x nb matrix
  • c is a mc x nc matrix
  • d is a md x nd matrix
  • order is an integer representing the number of occurences of c^T in the Kronecker products
  • ws is an instance of the IPlusAtKronBWs type

Version

  • 0.1.1

References

O. Kamenik (2005), "Solving SDGE models: A new algorithm for the Sylvester equation", Computational Economics 25, 167--187.