An iterative procedure for solving the Riccati equation A₂R - RA₁ = A₃ + RA₄R

• Autorzy: M. Thamban Nair
• Języki publikacji: EN

Abstrakty

EN

Let X₁ and X₂ be complex Banach spaces, and let A₁ ∈ BL(X₁), A₂ ∈ BL(X₂), A₃ ∈ BL(X₁,X₂) and A₄ ∈ BL(X₂,X₁). We propose an iterative procedure which is a modified form of Newton's iterations for obtaining approximations for the solution R ∈ BL(X₁,X₂) of the Riccati equation A₂R - RA₁ = A₃ + RA₄R, and show that the convergence of the method is quadratic. The advantage of the present procedure is that the conditions imposed on the operators A₁, A₂, A₃, A₄ are weaker than the corresponding conditions for Newton's iterations, considered earlier by Demmel (1987), Nair (1989) and Nair (1990) in the context of obtaining error bounds for approximate spectral elements. Also, we discuss an application of the procedure to spectral approximation under perturbations of the operator.

Kategorie tematyczne

• 45B05: Fredholm integral equations
• 65F35: Matrix norms, conditioning, scaling
• 65R20: Integral equations
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 147
• Numer: 1
• Strony: 15-26

Daty

wydano

2001

Twórcy

autor

M. Thamban Nair

• Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India

Identyfikatory

DOI

10.4064/sm147-1-2