Drazin inverse based numerical methods for singular linear differential systems
نویسندگان
چکیده
منابع مشابه
Orthogonal polynomials and semi-iterative methods for the Drazin-inverse solution of singular linear systems
In this work we present a novel class of semi-iterative methods for theDrazin-inverse solution of singular linear systems,whether consistent or inconsistent. The matrices of these systems are allowed to have arbitrary index and arbitrary spectra in the complex plane. The methods we develop are based on orthogonal polynomials and can all be implemented by 4-term recursion relations independently...
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Two numerical methods one continuous and the other discrete are proposed for solving inverse singular value problems The rst method consists of solving an ordinary di erential equation obtained from an explicit calculation of the projected gradient of a certain objective function The second method generalizes an iterative process proposed originally by Friedland et al for solving inverse eigenv...
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In a recent work by the author [Linear Algebra Appl. 298 (1999) 99] Krylov subspace methods were derived for the Drazin-inverse solution of consistent or inconsistent linear systems of the form Ax = b, where A ∈ CN×N is a singular and in general non-hermitian matrix that has an arbitrary index. One of these methods, modeled after the generalized conjugate residual method (GCR) and denoted DGCR,...
متن کاملAdditional results on index splittings for Drazin inverse solutions of singular linear systems
Given an n × n singular matrix A with Ind(A) = k, an index splitting of A is one of the form A = U − V , where R(U) = R(Ak) and N(U) = N(Ak). This splitting, introduced by the first author, generalizes the proper splitting proposed by Berman and Plemmons. Regarding singular systems Au = f , the first author has shown that the iterations u(i+1) = U#V u(i) + U#f converge to ADf , the Drazin inver...
متن کاملA unified approach to Krylov subspace methods for the Drazin-inverse solution of singular nonsymmetric linear systems
Consider the linear system Ax = b, where A ∈ CN×N is a singular matrix. In the present work we propose a general framework within which Krylov subspace methods for Drazininverse solution of this system can be derived in a convenient way. The Krylov subspace methods known to us to date treat only the cases in which A is hermitian and its index ind(A) is unity necessarily. In the present work A i...
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ژورنال
عنوان ژورنال: Advances in Engineering Software
سال: 2012
ISSN: 0965-9978
DOI: 10.1016/j.advengsoft.2012.04.001