Given a symmetrix positive definite matrix Q and a non-singular matrix L, Find symmetric positive definite solution X such that X = Q + L (X inv) L^T.
library(SolveRationalMatrixEquation) Q <- rbind(c(2,-1,0),c(-1,2,1),c(0,1,2)) L <- rbind(c(2,-2,18),c(2,1,0),c(1,2,0)) ##QR Decomposition QRdecompose(L) ##LQ Decompostion LQdecompose(L) ##Solve Rational Matrix X <- sol.rationalmatrix.euqation(Q, L) #Checking the results X - (Q + L %*% solve(X) %*% t(L))
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