Yuli Eidelman

A modification of the Dewilde-van der Veen method for inversion of finite structured matrices

Abstract We study a class of block structured matrices R ={ R ij } i , j =1 N with a property that the solution of the corresponding system Rx = y of linear algebraic equations may be performed for O( N ) arithmetic operations. In this paper for finite invertible matrices we analyze in detail factorization and inversion algorithms. These algorithms are related to those suggested by P.M. Dewilde and A.J. van der Veen (Time-varying Systems and Computations, Kluwer Academic Publishers, New York, 1998) for a class of finite and infinite matrices with a small Hankel rank. The algorithms presented here are more transparent and are a modification of the algorithms from the above reference. The approach and the proofs are essentially different from those in the above-mentioned reference. The paper contains also analysis of complexity and results of numerical experiments.

Fast QR Eigenvalue Algorithms for Hessenberg Matrices Which Are Rank-One Perturbations of Unitary Matrices

Let

Fast inversion algorithms for a class of structured operator matrices

\mathcal H_n\subset \mathbb C^{n\times n}

Efficient eigenvalue computation for quasiseparable Hermitian matrices under low rank perturbations

be the class of

A Fast Björck-Pereyra-Type Algorithm for Solving Hessenberg-Quasiseparable-Vandermonde Systems

n\times n

Implicit QR for Companion-like Pencils

Hessenberg matrices

Fast Inversion of Polynomial-Vandermonde Matrices for Polynomial Systems Related to Order One Quasiseparable Matrices

A

The unitary completion and QR iterations for a class of structured matrices

which are rank-one modifications of a unitary matrix, that is,

A Traub-like algorithm for Hessenberg-quasiseparable-Vandermonde matrices of arbitrary order

A=H +\B u\B w^H

Fast recursive algorithm for a class of structured matrices

, where