# lyapunov: Solve Lyapunov Equation In maotai: Tools for Matrix Algebra, Optimization and Inference

## 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

 1 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

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ## 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)