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MATHICSE Technical Report: Block Krylov subspace methods for functions of matrices II: Modified block FOM

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Linear Estimation

Ali H. Sayed

This textbook is intended for a graduate-level course and assumes familiarity with basic concepts from matrix theory, linear algebra, and linear system theory. Six appendices at the end of the book provide the reader with enough background and review mater ...

Prentice Hall2000

Complex WKB method for 3-level scattering systems

Charles Pfister

In this note the S‐matrix naturally associated with a singularly perturbed three‐dimensional system of linear differential equations without turning point on the real axis is considered. It is shown that for a fairly large class of examples, the Complex WK ...

2000

A recursive method for solving unconstrained tangential interpolation problems

Ali H. Sayed

An efficient recursive solution is presented for the one-sided unconstrained tangential interpolation problem. The method relies on the triangular factorization of a certain structured matrix that is implicitly defined by the interpolation data. The recurs ...

IEEE1999

From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex

Jan Sickmann Hesthaven

The electrostatic interpretation of the Jacobi-Gauss quadrature points is exploited to obtain interpolation points suitable for approximation of smooth functions defined on a simplex. Moreover, several new estimates, based on extensive numerical studies, f ...

Society for Industrial and Applied Mathematics1998

On the zeros of discrete-time linear periodic systems

Giancarlo Ferrari Trecate

Discrete-time linear periodic SISO systems having uniform relative degree are considered. A closed-form expression of the blocking input is derived and exploited to obtain a computationally advantageous characterisation of the structural zeros. Indeed, it ...

1997

A recursive Schur-based solution of the four-block problem

Ali H. Sayed

We describe a new solution to the four-block problem using the method of generalized Schur analysis. We first reduce the general problem to a simpler one by invoking a coprime factorization with a block-diagonal inner matrix. Then, using convenient spectra ...

IEEE1994

Recursive solutions of rational interpolation problems via fast matrix factorization

Ali H. Sayed

We describe a novel approach to analytic rational interpolation problems of the Hermite-Fejér type, based on the fast generalized Schur algorithm for the recursive triangular factorization of structured matrices. We use the interpolation data to construct ...

Birkhäuser Basel1994

Structured matrices and unconstrained rational interpolation problems

Ali H. Sayed

We describe a fast recursive algorithm for the solution of an unconstrained rational interpolation problem by exploiting the displacement structure concept. We use the interpolation data to implicitly define a convenient non-Hermitian structured matrix, an ...

North-Holland1994

Time-variant displacement structure and interpolation problems

Ali H. Sayed

Derives a new recursive solution for a general time-variant interpolation problem of the Hermite-Fejer type, based on a fast algorithm for the recursive triangular factorization of time-variant structured matrices. The solution follows from studying the pr ...

IEEE1994

Displacement structure and rational interpolation theory

Ali H. Sayed

We derive square-root based algorithms for structures matrices and discuss potential applications to interpolation problems. The mathematical machinery used here is based on a standard Gaussian elimination technique and on simple results from matrix and li ...

1993