lyapunov: Solve Lyapunov Equation

In maotai: Tools for Matrix Algebra, Optimization and Inference

Solve Lyapunov Equation

Description

The Lyapunov equation is of form

AX + XA^\top = Q

where A and Q are square matrices of same size. Above form is also known as continuous form. This is a wrapper of armadillo's sylvester function.

Usage

lyapunov(A, Q)

Arguments

A	a (p\times p) matrix as above.
Q	a (p\times p) matrix as above.

Value

a solution matrix X of size (p\times p).

References

\insertRef

sanderson_armadillo_2016maotai

\insertRef

eddelbuettel_rcpparmadillo_2014maotai

Examples

## simulated example
#  generate square matrices
A = matrix(rnorm(25),nrow=5)
X = matrix(rnorm(25),nrow=5)
Q = A%*%X + X%*%t(A)

#  solve using 'lyapunov' function
solX = lyapunov(A,Q)
## Not run: 
pm1 = "* Experiment with Lyapunov Solver"
pm2 = paste("* Absolute Error  : ",norm(solX-X,"f"),sep="")
pm3 = paste("* Relative Error  : ",norm(solX-X,"f")/norm(X,"f"),sep="")
cat(paste(pm1,"\n",pm2,"\n",pm3,sep=""))

## End(Not run)

maotai documentation built on March 31, 2023, 6:48 p.m.