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Cover image for Numerical methods for structured matrices and applications : the Georg Heinig memorial volume
Title:
Numerical methods for structured matrices and applications : the Georg Heinig memorial volume
Series:
Operator theory : advances and applications ; 199
Publication Information:
Basel : Birkhäuser, 2010
Physical Description:
viii, 439 p. : ill. ; 24 cm.
ISBN:
9783764389956
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30000010236891 QA188 N844 2010 Open Access Book Book
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Summary

Summary

Georg Heing, a charming, erudite man, and a ?rst rate mathematician died un- pectedly of a heart attack on May 10, 2005. Georg is survived by his wife Gerti, his daughter Susanne, and his son Peter. We have lost one the leading experts in the ?eld of structured matrices, a wonderful colleague, and a terri?c friend. GeorgHeinig sresults, approaches, andhisscienti?ctastein?uencedourc- munity of researchers working on structured matrices. In fact, the community s focus grew to re?ect his interdisciplinary vision ranging from applications (e.g., in systems and control theory and signal processing) through fundamental mat- matics(structuredmatrices, periodicJacobi, Toeplitz, andWiener-Hopfoperators, classesofsingularintegraloperators, resultantsandBezoutiansforoperator-valued polynomials and continual analogs thereof) to numerical analysis and fast al- rithms. The broad spectrum of Georg Heinig s interests are represented in this collection. Georg served as an Associate Editor of two top journals: Integral Equations andOperatorTheoryand LinearAlgebraand Its Applications. This volumestarts with two eulogies published earlier by IEOT and LAA. The ?rst one, published in IEOT is by Albrecht Bot ] tcher, Israel Gohberg (who was Georg s advisor during his Ph.D. studies), and Bernd Silbermann. The second one, published in LAA is by Karla Rost who collaborated with Georg during last three decades until day of his death. They have produced together more than 30 papers and a monograph."


Table of Contents

A. Böttcher and I. Gohberg and B. SilbermannK. RostG. Heinig and K. RostT. Amdeberhan and G. HeinigT. Bella and Y. Eidelman and I. Gohberg and V. Olshevsky and E. Tyrtyshnikov and P. ZhlobichD.A. Bini and P. BoitoV. BolotnikovA. Böttcher and S. GrudskyE. Bozzo and D. FasinoV. Cortées and J.M. PeñaS. Delvaux and L. Gemignani and M. Van BarelS. FeldmannB. Fritzsche and B. Kirstein and A. LasarowB. Fritzsche and B. Kirstein and L.A. SakhnovichJ. Jain and H. Li and C.-K. Koh and V. BalakrishnanV.Y. Pan and B.J. Murphy and R.E. RosholtC. Tablino PossioS.M. Rump and H. SekigawaY. V. ShlapakE. Tyrtyshnikov
Forewordp. vii
Part I Georg Heinig
Georg Heinig (1947-2005) In Memoriamp. 3
Georg Heinig, November 24, 1947 - May 10, 2005 A Personal Memoir and Appreciationp. 7
Introduction to Bezoutiansp. 25
On Matrices that are not Similar to a Toeplitz Matrix and a Family of Polynomialsp. 119
Part II Research Contributions
A Traub-like Algorithm for Hessenberg-quasi-separable-Vandermonde Matrices of Arbitrary Orderp. 127
A Fast Algorithm for Approximate Polynomial GCD Based on Structured Matrix Computationsp. 155
On Inertia of Some Structured Hermitian Matricesp. 175
Variable-coefficient Toeplitz Matrices with Symbols beyond the Wiener Algebrap. 191
A Priori Estimates on the Structured Conditioning of Cauchy and Vandermonde Matricesp. 203
Factorizations of Totally Negative Matricesp. 221
QR-factorization of Displacement Structured Matrices Using a Rank Structured Matrix Approachp. 229
Bezoutians Applied to Least Squares Approximation of Rational Functionsp. 255
On the Weyl Matrix Balls Corresponding to the Matricial Carathéodory Problem in Both Nondegenerate and Degenerate Casesp. 289
On Extremal Problems of Interpolation Theory with Unique Solutionp. 333
O(n) Algorithms for Banded Plus Semiseparable Matricesp. 347
Unified Nearly Optimal Algorithms for Structured Integer Matricesp. 359
V-cycle Optimal Convergence for DCT-III Matricesp. 377
The Ratio Between the Toeplitz and the Unstructured Condition Numberp. 397
A New Algorithm for Finding Positive Eigenvectors for a Class of Nonlinear Operators Associated with M-matricesp. 421
Hankel Minors and Pade Approximationsp. 431
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