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158
Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization
, 2000
"... ..."
Solving Systems of Polynomial Equations
 AMERICAN MATHEMATICAL SOCIETY, CBMS REGIONAL CONFERENCES SERIES, NO 97
, 2002
"... One of the most classical problems of mathematics is to solve systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely applied across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, ..."
Abstract

Cited by 221 (14 self)
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One of the most classical problems of mathematics is to solve systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely applied across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory
The Quadratic Eigenvalue Problem
, 2001
"... . We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skewHermitian) and t ..."
Abstract

Cited by 262 (21 self)
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. We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skew
On the decay rate of Hankel singular values and related issues
 CONTROL LETT
, 2002
"... This paper investigates the decay rate of the Hankel singular values of linear dynamical systems. This issue is of considerable interest in model reduction by means of balanced truncation, for instance, since the sum of the neglected singular values provides an upper bound for an appropriate norm of ..."
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Cited by 63 (6 self)
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This paper investigates the decay rate of the Hankel singular values of linear dynamical systems. This issue is of considerable interest in model reduction by means of balanced truncation, for instance, since the sum of the neglected singular values provides an upper bound for an appropriate norm
Numerical Computation Of A Polynomial GCD And Extensions
, 1996
"... In the first part of this paper, we dene approximate polynomial gcds (greatest common divisors) and extended gcds provided that approximations to the zeros of the input polynomials are available. We relate our novel definition to the older and weaker ones, based on perturbation of the coefficients o ..."
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Cited by 21 (5 self)
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of the input polynomials, we demonstrate some deficiency of the latter definitions (which our denition avoids), and we propose new effective sequential and parallel (RNC and NC) algorithms for computing approximate gcds and extended gcds. Our stronger results are obtained with no increase of the asymptotic
SUMS OF SQUARES, MOMENT MATRICES AND OPTIMIZATION OVER POLYNOMIALS
, 2008
"... Citation for published version (APA): ..."
Fast fractionfree triangularization of Bezoutians with applications to subresultant chain computation
, 1997
"... An algorithm for the computation of the LU factorization over the integers of an n \Theta n Bezoutian B is presented. The algorithm requires O(n 2 ) arithmetic operations and involves integers having at most O(n log nc) bits, where c is an upper bound of the moduli of the integer entries of B. As ..."
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Cited by 3 (1 self)
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. As an application, by using the correlations between Bezoutians and the Euclidean scheme, we devise a new divisionfree algorithm for the computation of the polynomial pseudoremainder sequence of two polynomials of degree at most n in O(n 2 ) arithmetic operations. The growth of the length of the integers
A Fast Iterative Method for Determining the Stability of a Polynomial
"... We present an iterative numerical method for solving two classical stability problems for a polynomial p(x) of degree n: the RouthHurwitz and the SchurCohn problems. This new method relies on the construction of a polynomial sequence fp (k) (x)g k2N , p (0) (x) = p(x) , such that p (k) (x) ..."
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Cited by 1 (0 self)
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) quadratically converges to (x \Gamma 1) p (x + 1) n\Gammap whenever the starting polynomial p(x) has p zeros with positive real parts and n \Gamma p zeros with negative real parts. By combining some new results on structured matrices with the fast polynomial arithmetic, we prove that the coefficients of p
Results 1  10
of
158