README.md

SolveIPlusOrMinusAkronB.jl

THIS PACKAGE HAS BEEN RENAMED GeneralizedSylvesterSolver.jl

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 1.5

using Pkg
Pkg.add(url="https://git.dynare.org/julia-packages/FastLapackInterface.jl")
Pkg.add(url="https://git.dynare.org/julia-packages/QUT")
Pkg.add(url="https://git.dynare.org/julia-packages/KroneckerTools.jl")
Pkg.add(url="https://git.dynare.org/julia-packages/SolveIPlusOrMinusAKronB.jl")

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

• 0.1.0

References

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