Browsing by Author "Lancaster, Peter"
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Item Embargo A Spectral decomposition for a polynomial operator(1968) Pattabhiraman, M. V.; Lancaster, PeterItem Open Access Analysis and modification of Newton's method for algebraic riccati equations(1998) Guo, Chun-Hua; Lancaster, PeterItem Open Access Analytic perturbation theory for matrix functions(2003) Zhou, Fei; Lancaster, PeterItem Open Access Blending functions and finite elements(1974) Watkins, David Scott; Lancaster, PeterItem Embargo Equivalence of quadratic performance indices for linear optimal control systems(1973) Kolowrocki, Wojciech; Lancaster, PeterItem Open Access Linear operations in Krein spaces(1995) Zizler, Petr; Lancaster, PeterItem Embargo Numerical and theoretical studies of eigenvalue problems of mathematical physics(1975) Terray, John R.; Lancaster, PeterItem Embargo On the distribution of the characteristic roots of stochastic and doubly-stochastic matrices(1974) Plaxton, Audrey Grace Louise; Lancaster, PeterItem Embargo Practical and theoretical studies in numerical error analysis(1970) Rokne, J. (Jon), 1941-; Lancaster, PeterItem Open Access Spectral properties of diagonally dominant infinite matrices(1988) Farid, Farid Omar; Lancaster, PeterItem Embargo Square roots of linear transformations(1976) Cross, Gerald William; Lancaster, PeterItem Embargo Stability criteria for the solution of the system x(t)(1968) Street, A. V.; Lancaster, PeterItem Embargo Surface representation by finite elements(1978) Ritchie, Susan I. M.; Lancaster, PeterItem Open Access Variational principles and numerical algorithms for symmetric matrix pencils(1989) Ye, Qiang; Lancaster, PeterThis thesis concerns the eigenvalue problems for symmetric ( or hermitian) matrix pencils lambda A-B in which A is nonsingular and neither A nor B is definite. Our intention is to find out to what extent some classical theoretical results and numerical algorithms for symmetric matrices can be carried over to symmetric pencils. First, a spectral characterization of definite pencils is presented, and an inertia function is introduced and used to give a simple algorithm for finding a positive definite matrix in a definite pencil. Then the minimax theorems are developed in Chapter 2 and its application to positive semidefinite perturbations is included. Following that, we study the numerical methods. The Rayleigh quotient iteration is introduced and the local and global convergence properties are established. Moreover, a method based on minimization of the Rayleigh quotients is proposed for definite pencils. Then the Rayleigh-Ritz method is formulated for the symmetric pencil problem, and using Krylov subspaces, an approximation error bound is proved. In particular, Lanczos' algorithm is discussed and a convergence criterion is demonstrated by using residuals or by a local perturbation expansion.