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Time-variant displacement structure and interpolation problems

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Generalized Interpolation: Higher Quality at no Additional Cost

Michaël Unser, Philippe Thévenaz, Thierry Blu

We extend the classical interpolation method to generalized interpolation. This extension is done by replacing the interpolating function by a non-interpolating function that is applied to prefiltered data, in order to preserve the interpolation condition. ...

IEEE1999

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

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

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

Lattice structures for time-variant interpolation problems

Ali H. Sayed

The authors derive a 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 ...

1992

Recursive solutions to rational interpolation problems

Ali H. Sayed

Describe a straightforward recursive and global approach for the solution of rational interpolation problems. The derivation is based on a simple and well known matrix identity, namely, the Schur reduction procedure, and exploits connections with structure ...

1992

A Schur-based approach to the four-block problem

Ali H. Sayed

We descibe an alternative 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 an inner-outer factorization with a block-diagonal inner matrix. Then using smal ...

1992

Consistency, Stability, a-Priori and a-Posteriori Errors for Nonlinear Problems

Jacques Rappaz

In an abstract framework similar to the one developed in Crouzeix-Rappaz [2], we present a formalism which makes precise the notions of consistency and stability for the finite element approximation of nonlinear elliptic problems. The consistency is connec ...

1991

Design, transformation and animation of human faces

Daniel Thalmann

Creation of new human faces for synthetic actors is a difficult task. The situation may be improved by introducing tools for the creation. Three approaches are discussed: modification and edition of an existing synthetic actor using local transformations; ...

1989