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Kinetic Euclidean Distance Matrices

Publications associées (39)

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On Matrix Rigidity and the Complexity of Linear Forms

Mahdi Cheraghchi Bashi Astaneh

The rigidity function of a matrix is defined as the minimum number of its entries that need to be changed in order to reduce the rank of the matrix to below a given parameter. Proving a strong enough lower bound on the rigidity of a matrix implies a nontri ...

2005

Low Rank Updates for the Cholesky Decomposition

Matthias Seeger

Usage of the Sherman-Morrison-Woodbury formula to update linear systems after low rank modifications of the system matrix is widespread in machine learning. However, it is well known that this formula can lead to serious instabilities in the presence of ro ...

2004

A fast algorithm for subspace state-space system identification via exploitation of the displacement structure

Daniel Kressner

Two recent approaches (Van Overschee, De Moor, N4SID, Automatica 30 (1) (1994) 75; Verhaegen, Int. J. Control 58(3) (1993) 555) in subspace identification problems require the computation of the R factor of the QR factorization of a block-Hankel matrix H, ...

Elsevier2001

A survey of spectral factorization methods

Ali H. Sayed

Spectral factorization is a crucial step in the solution of linear quadratic estimation and control problems. It is no wonder that a variety of methods has been developed over the years for the computation of canonical spectral factors. This paper provides ...

Wiley-Blackwell2001

Displacement Structure and H ∞ Problems

Ali H. Sayed

The solution of H∞ problems requires the determination of contractive operators that map certain input signals to certain output signals. Such operators, and tests for their contractiveness, arise naturally in a scattering formulation of the generalized Sc ...

Springer2000

Many important problems in pure and applied mathematics and engineering can be reduced to linear algebra on dense structured matrices. The structure of these dense matrices is understood in the sense that their n2 entries can be "compressed" to a smaller n ...

2000

EP theorems and linear complementary problems

Let A be a rational n × n square matrix and b be a rational n-vector for some positive integer n. The linear complementarity problem (abbreviated by LCP) is to find a vector (x, y) in R^(2n) satisfying y = Ax + b (x, y) >= 0 and the complementarity conditi ...

1998

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

A Stable and Efficient Algorithm for the Indefinite Linear Least-Squares Problem

Ali H. Sayed

We develop an algorithm for the solution of indefinite least-squares problems. Such problems arise in robust estimation, filtering, and control, and numerically stable solutions have been lacking. The algorithm developed herein involves the QR factorizatio ...

Society for Industrial and Applied Mathematics1998

The traditional approach to the parallelization of linear algebra algorithms such as matrix multiplication and LU factorization calls for static allocation of matrix blocks to processing elements (PEs). Such algorithms suffer from two drawbacks: they are v ...

Springer-Verlag1997