Numerical Methods for Structured Matrices and Applications

This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to topics such as fast algorithms, in which the late Georg Heinig made outstanding achievements.

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.

In honor of Georg Heinig, one of the leading experts in the field of structured matrices, an irreplaceable colleague, and Includes supplementary material: sn.pub/extras

Inhalt
Georg Heinig.- Georg Heinig (19472005) In Memoriam.- Georg Heinig November 24, 1947 - May 10, 2005 A Personal Memoir and Appreciation.- to Bezoutians.- On Matrices that are not Similar to a Toeplitz Matrix and a Family of Polynomials Tewodros Amdeberhan and Georg Heinig.- Research Contributions.- A Traub-like Algorithm for Hessenbergquasiseparable- Vandermonde Matrices of Arbitrary Order.- A Fast Algorithm for Approximate Polynomial GCD Based on Structured Matrix Computations.- On Inertia of Some Structured Hermitian Matrices.- Variable-coefficient Toeplitz Matrices with Symbols beyond the Wiener Algebra.- A Priori Estimates on the Structured Conditioning of Cauchy and Vandermonde Matrices.- Factorizations of Totally Negative Matrices.- QR-factorization of Displacement Structured Matrices Using a Rank Structured Matrix Approach.- Bezoutians Applied to Least Squares Approximation of Rational Functions.- On the Weyl Matrix Balls Corresponding to the Matricial Carathéodory Problem in Both Nondegenerate and Degenerate Cases.- On Extremal Problems of Interpolation Theory with Unique Solution.- O(n) Algorithms for Banded Plus Semiseparable Matrices.- Unified Nearly Optimal Algorithms for Structured Integer Matrices.- V-cycle Optimal Convergence for DCT-III Matrices.- The Ratio Between the Toeplitz and the Unstructured Condition Number.- A New Algorithm for Finding Positive Eigenvectors for a Class of Nonlinear Operators Associated with M-matrices.- Hankel Minors and Pade Approximations.