README.md

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.