Residual bounds of approximate solutions of the algebraic Riccati equation
1997 (English)In: Numerische Mathematik, Vol. 76, no 2, 249-263 p.Article in journal (Refereed) Published
Let (X) over tilde greater than or equal to 0 approximate the unique Hermitian positive semi-definite solution X to the algebraic Riccati equation (ARE) G + A(H)X + XA -XFX = 0, where F, G greater than or equal to 0, (A, F) is stabilizable, and (A, G) is detectable. Let (R) over cap = G + A(H) (X) over tilde + (X) over tilde A - (X) over tilde F (X) over tilde be the residual of the ARE with respect to (X) over tilde, and define the linear operator L by LH = (A - F (X) over tilde(H)H + H(A - F (X) over tilde), H = H-H is an element of C-nxn. By applying a new forward perturbation bound to the optimal backward perturbation corresponding to the approximate solution (X) over tilde, we obtained the following result: If A - F (X) over tilde is stable, and if 4 parallel to L(-1)parallel to parallel to L-1(R) over cap parallel to parallel to(F parallel to < 1 for any unitarily invariant norm parallel to parallel to, then [GRAPHICS] oth solution. Numerical examples illustrate and supplement the analysis.
Place, publisher, year, edition, pages
1997. Vol. 76, no 2, 249-263 p.
IdentifiersURN: urn:nbn:se:umu:diva-22003ISBN: 0029-599XOAI: oai:DiVA.org:umu-22003DiVA: diva2:212266