Download or read book Asymptotic Distribution of the Zeros of Faber Polynomials written by Arnoldus Bernardus Jacobus Kuijlaars and published by . This book was released on 1994 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Using potential theoretic methods and exploiting the connection with eigenvalues of Toeplitz matrices, we investigate the limiting behavior of zeros of Faber polynomials generated by a Laurent series. Our results build upon fundamental work of J.L. Ullman. For example, we show that if E is a compact set with simply connected complement and connected interior whose boundary is either (i) not a piecewise analytic curve or (ii) a piecewise analytic curve but with a singularity other than an outward cusp, then the equilibrium distribution for E is a limit measure of the sequence of normalized zero counting measures for the Faber polynomials associated with E."
Download or read book Asymptotic Distribution of Zeros of Approximating Polynomials written by Mehrdad Simkani and published by . This book was released on 1987 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Exploiting Symmetry in Applied and Numerical Analysis written by Eugene L. Allgower and published by American Mathematical Soc.. This book was released on 1993 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry plays an important role in theoretical physics, applied analysis, classical differential equations, and bifurcation theory. Although numerical analysis has incorporated aspects of symmetry on an ad hoc basis, there is now a growing collection of numerical analysts who are currently attempting to use symmetry groups and representation theory as fundamental tools in their work. This book contains the proceedings of an AMS-SIAM Summer Seminar in Applied Mathematics, held in 1992 at Colorado State University. The seminar, which drew about 100 scientists from around the world, was intended to stimulate the systematic incorporation of symmetry and group theoretical concepts into numerical methods. The papers in this volume have been refereed and will not be published elsewhere.
Download or read book Introduction To The Theory Of Weighted Polynomial Approximation written by H N Mhaskar and published by World Scientific. This book was released on 1997-01-04 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we have attempted to explain a variety of different techniques and ideas which have contributed to this subject in its course of successive refinements during the last 25 years. There are other books and surveys reviewing the ideas from the perspective of either potential theory or orthogonal polynomials. The main thrust of this book is to introduce the subject from an approximation theory point of view. Thus, the main motivation is to study analogues of results from classical trigonometric approximation theory, introducing other ideas as needed. It is not our objective to survey the most recent results, but merely to introduce to the readers the thought processes and ideas as they are developed.This book is intended to be self-contained, although the reader is expected to be familiar with rudimentary real and complex analysis. It will also help to have studied elementary trigonometric approximation theory, and have some exposure to orthogonal polynomials.
Download or read book Series of Faber Polynomials written by P.K. Suetin and published by CRC Press. This book was released on 1998-03-23 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents some important classical and modern results of the series of Faber polynomials and their applications. Interest in this subject has increased rapidly over the last decade, although the presentation of research has, until now, been confined mainly to journal articles. Applications include theory of functions of complex variables, theory of analytic function approximation, and some aspects of numerical analysis.
Download or read book A Note on Asymptotic Zero Distribution of Orthogonal Polynomials written by William F. Trench and published by . This book was released on 2018 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: We strengthen a theorem of Kuijlaars and Serra Capizzano on the distribution of zeros of a sequence of orthogonal polynomials for which the coefficients in the three term recurrence relation are clustered at finite points. The proof uses a matrix argument motivated by a theorem of Tyrtyshnikov.
Download or read book Asymptotics for Orthogonal Polynomials written by Walter Van Assche and published by Springer. This book was released on 2006-11-14 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently there has been a great deal of interest in the theory of orthogonal polynomials. The number of books treating the subject, however, is limited. This monograph brings together some results involving the asymptotic behaviour of orthogonal polynomials when the degree tends to infinity, assuming only a basic knowledge of real and complex analysis. An extensive treatment, starting with special knowledge of the orthogonality measure, is given for orthogonal polynomials on a compact set and on an unbounded set. Another possible approach is to start from properties of the coefficients in the three-term recurrence relation for orthogonal polynomials. This is done using the methods of (discrete) scattering theory. A new method, based on limit theorems in probability theory, to obtain asymptotic formulas for some polynomials is also given. Various consequences of all the results are described and applications are given ranging from random matrices and birth-death processes to discrete Schrödinger operators, illustrating the close interaction with different branches of applied mathematics.
Download or read book Mathematics of Computation 1943 1993 A Half Century of Computational Mathematics written by Walter Gautschi and published by American Mathematical Soc.. This book was released on 1994 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of an International Conference held in Vancouver, B.C., August 1993, to commemorate the 50th anniversary of the founding of the journal Mathematics of Computation. It consisted of a Symposium on Numerical Analysis and a Minisymposium of Computational Number Theory. This proceedings contains 14 invited papers, including two not presented at the conference--an historical essay on integer factorization, and a paper on componentwise perturbation bounds in linear algebra. The invited papers present surveys on the various subdisciplines covered by Mathematics of Computation, in a historical perspective and in a language accessible to a wide audience. The 46 contributed papers address contemporary specialized work. Annotation copyright by Book News, Inc., Portland, OR
Download or read book Computational Methods and Function Theory written by and published by . This book was released on 2008 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hyponormal Quantization of Planar Domains written by Björn Gustafsson and published by Springer. This book was released on 2017-09-29 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz potential at critical exponent, is at the heart of this novel framework; its best rational approximants unveil a new class of complex orthogonal polynomials whose asymptotic distribution of zeros is thoroughly studied in the text. Connections with areas of potential theory, approximation theory in the complex domain and fluid mechanics are established. The text is addressed, with specific aims, at experts and beginners in a wide range of areas of current interest: potential theory, numerical linear algebra, operator theory, inverse problems, image and signal processing, approximation theory, mathematical physics.
Download or read book Chebyshev Quadrature for Measures with a Strong Singularity written by Arnoldus Bernardus Jacobus Kuijlaars and published by . This book was released on 1994 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We give examples of measures admitting Chebyshev quadrature that have a singular behavior near one end point. In our main result we present such a measure on [0, 1] whose density behaves like t−1(log t)−2 as t -> 0. These examples are derived from results of He and Saff on the zeros of Faber polynomials associated with an m-cusped hypocycloid. We also give a formula for the asymptotic distribution of these zeros."
Download or read book On the Asymptotic Properties of Extremal Polynomials with Prescribed Constant Term written by J. L. Walsh and published by . This book was released on 1960 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Zeros Of Laguerre Polynomials written by Ayo Odeniran and published by . This book was released on 2016-09-07 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific Essay from the year 2011 in the subject Mathematics - Algebra, language: English, abstract: In this work, we make an attempt to gather different results by many mathematicians who have made landmark achievements in studies on zeros of Laguerre polynomials. We discuss bounds for extreme zeros of some classical orthogonal polynomials, bounds for zeros of the Laguerre polynomials where we quote the works of Ilia Krasikov, among others. The quoted works are: "Limit relation for the complex zeros of Laguerre polynomials," "On the Asymptotic Distribution of the Zeros of Laguerre Polynomials," "Monotonicity of zeros of Laguerre polynomials," "Zeros of linear combinations of Laguerre polynomials from different sequences," "Linear combinations of Laguerre polynomials of the same degree," "Linear combinations of Laguerre polynomials of different degree" and "Convexity of the extreme zeros of Laguerre polynomials."
Download or read book Asymptotic Properties of Polynomials with Auxiliary Conditions of Interpolation written by Joseph Leonard Walsh and published by . This book was released on 1961 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let a closed bounded point set E be given in the z-plane. Necessary and sufficient conditions are found for validity of the following: given assigned conditions of interpolation in a finite number of points: pn(zk) = Ank; there exists a sequence of polynomials pn(z) satisfying these conditions and lim sup max pn(z), z on E 1/n = (E), where (E) is the transfinite diameter of E. (Author).
Download or read book Sarajevo Journal of Mathematics written by and published by . This book was released on 2005 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Zeros of Faber Polynomials Generated by an M star written by Arnoldus Bernardus Jacobus Kuijlaars and published by . This book was released on 1994 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "It is shown that the zeros of the Faber polynomials generated by a regular m-star are located on the m-star. This proves a recent conjecture of J. Bartolomeo and M. He. The proof uses the connection between zeros of Faber polynomials and Chebyshev quadrature formulas."
Download or read book Modern Trends in Constructive Function Theory written by E. B. Saff and published by American Mathematical Soc.. This book was released on 2016-03-31 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the conference Constructive Functions 2014, held in May 2014. The papers in this volume include results on polynomial approximation, rational approximation, Log-optimal configurations on the sphere, random continued fractions, ratio asymptotics for multiple orthogonal polynomials, the bivariate trigonometric moment problem, and random polynomials.
