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A block algorithm for computing antitriangular factorizations of symmetric matrices

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The Degenerate Bounded Errors-in-Variables Model

Ali H. Sayed

We consider the following problem:

\min_{x \in {\cal R}^n} \min_{\|E\| \le \eta} \|(A+E)x-b\|

, where A is an

m \times n

real matrix and b is an n-dimensional real column vector when it has multiple global minima. This problem is an errors-in-variables ...

2001

A Fast Stable Solver for Nonsymmetric Toeplitz and Quasi-Toeplitz Systems of Linear Equations

Ali H. Sayed

We derive a stable and fast solver for nonsymmetric linear systems of equations with shift structured coefficient matrices (e.g., Toeplitz, quasi-Toeplitz, and product of two Toeplitz matrices). The algorithm is based on a modified fast QR factorization of ...

Society for Industrial and Applied Mathematics1998

Stabilizing the Generalized Schur Algorithm

Ali H. Sayed

This paper provides a detailed analysis that shows how to stabilize the generalized Schur algorithm, which is a fast procedure for the Cholesky factorization of positive-definite structured matrices R that satisfy displacement equations of the form $R - FR ...

Society for Industrial and Applied Mathematics1996

Time-variant displacement structure and triangular arrays

Ali H. Sayed

The authors extend the concept of displacement structure to time-variant matrices and use it to efficiently and recursively propagate the Cholesky factor of such matrices. A natural implementation of the algorithm is via a modular triangular array of proce ...

IEEE1994

A state-space approach to adaptive RLS filtering

Ali H. Sayed

Adaptive filtering algorithms fall into four main groups: recursive least squares (RLS) algorithms and the corresponding fast versions; QR- and inverse QR-least squares algorithms; least squares lattice (LSL) and QR decomposition-based least squares lattic ...

Institute of Electrical and Electronics Engineers1994

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

Structure and arithmetic complexity of products and inverses of Toeplitz matrices

Martin Vetterli

We derive a formula for the product of two Toeplitz matrices that is similar to the Trench formula for the inverse of a Toeplitz matrix. We then derive upper and lower bounds for number of multiplications required to compute the inverse or the product of T ...

1991

The Degenerate Bounded Errors-in-Variables Model

Ali H. Sayed

We consider the following problem:

\min_{x \in {\cal R}^n} \min_{\|E\| \le \eta} \|(A+E)x-b\|

, where A is an

m \times n

real matrix and b is an n-dimensional real column vector when it has multiple global minima. This problem is an errors-in-variables ...

2001