Unit

Numerical Algorithms and High-Performance Computing - CADMOS Chair

Laboratory

Related publications (333)

On extremal behaviors of Murty's least index method

In this small note, we observe some extremal behaviors of Murty's least index method for solving linear complementarity problems. In particular, we show that the expected number of steps for solving Murty's exponential example with a random permutation of ...

1994

Time-variant structured matrices: An application to instrumental variable methods

Ali H. Sayed

We derive a recursive algorithm for the time-update of the triangular factors of non-Hermitian time-variant matrices with structure. These are matrices that undergo low-rank modifications as time progresses. special cases of which often arise in adaptive f ...

1994

Fast triangular factorization of the sum of quasi-Toeplitz and quasi-Hankel matrices

Ali H. Sayed

The literature contains several recent fast algorithms for the triangular factorization of strongly regular Toeplitz-plus-Hankel matrices. In this paper we study the rather more general sum of quasi-Toeplitz and quasi-Hankel matrices, both Hermitian and no ...

Elsevier1993

Iterative Toeplitz solvers with local quadratic convergence

Martin Vetterli

We study an iterative, locally quadratically convergent algorithm for solving Toeplitz systems of equations from [R. P. Brent, F. G. Gustavson and D. Y. Y. Yun. ''Fast solution of Toeplitz systems of equations and computation of Pade approximations'', J. A ...

1993

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

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

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

Structured matrices and fast RLS adaptive filtering

Ali H. Sayed

We present a new approach to the discrete-time Chandrasekhar recursions and some generalizations thereof. We extend the recursions to a class of structured time-variant state-space models, and discuss connections with the (generalized) Schur algorithm. We ...

Elsevier1992

Lattice filter interpretations of the Chandrasekhar recursions for estimation and spectral factorization

Ali H. Sayed

The authors use the classical Schur reduction procedure to give a lattice filter implementation of the Chandrasekhar recursions. The derivation is based on the observation that the covariance matrix of a process with a time-invariant state-space model is s ...

IEEE1992

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