Approximation and Computation: In Honor of Gradimir V. Milovanovic

ISBN-13: 9781461427032 / Angielski / Miękka / 2012 / 482 str.

Walter Gautschi; Giuseppe Mastroianni; Themistocles M. Rassias

Opis

Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovic, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Special features of this volume: - Presents results and approximation methods in various computational settings including: polynomial and orthogonal systems, analytic functions, and differential equations. - Provides a historical overview of approximation theory and many of its subdisciplines; - Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences. "Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in the computational and applied sciences.

Spis treści

Part I Introduction The Scientific Work of Gradimir V. Milovanović Aleksandar Ivić My Collaboration with Gradimir V. Milovanović Walter Gautschi On Some Major Trends in Mathematics Themistocles M. Rassias Part II Polynomials and Orthogonal Systems An Application of Sobolev Orthogonal Polynomials to the Computation of a Special Hankel Determinant Paul Barry, Predrag M. Rajković and Marko D. Petković Extremal Problems for Polynomials in the Complex Plane Borislav Bojanov Energy of Graphs and OrthogonalMatrices V. Božin and M. Mateljević Interlacing Property of Zeros of Shifted Jacobi Polynomials Aleksandar S. Cvetković Trigonometric Orthogonal Systems Aleksandar S. Cvetković and Marija P. Stanić Experimental Mathematics Involving Orthogonal Polynomials Walter Gautschi Compatibility of Continued Fraction Convergents with Padé Approximants Jacek Gilewicz and Radosław Jedynak Orthogonal Decomposition of Fractal Sets Ljubiša M. Kocić, Sonja Gegovska - Zajkova, Elena Babače Positive Trigonometric Sums and Starlike Functions Stamatis Koumandos Part III Quadrature Formulae Quadrature Rules for Unbounded Intervals and Their Application to Integral Equations G. Monegato, L. Scuderi Gauss-Type Quadrature Formulae for Parabolic Splines with Equidistant Knots Geno Nikolov and Corina Simian Approximation of the Hilbert Transform on the Real Line Using Freud Weights Incoronata Notarangelo The Remainder Term of Gauss-Tur´an Quadratures for Analytic Functions Miodrag M. Spalević and Miroslav S. Pranić Towards a General Error Theory of the Trapezoidal Rule JörgWaldvogel Part IV Differential Equations Finite Difference Method for a Parabolic Problem with Concentrated Capacity and Time-Dependent Operator Dejan R. Bojović and Boško S. Jovanović Adaptive Finite Element Approximation of the Francfort-MarigoModel of Brittle Fracture Siobhan Burke, Christoph Ortner and Endre Süli A NyströmMethod for Solving a Boundary Value Problems on [0, ) Carmelina Frammartino Finite Difference Approximation of a Hyperbolic Transmission Problem Boško S. Jovanović Homeomorphisms and Fredholm Theory for Perturbations of Nonlinear Fredholm Maps of Index Zero and of A-Proper Maps with Applications P. S. Milojević Singular Support and FLq Continuity of Pseudodifferential Operators Stevan Pilipović, Nenad Teofanov and Joachim Toft On a Class of Matrix Differential Equations with Polynomial Coefficients Boro M. Piperevski Part V Applications Optimized Algorithm for Petviashvili’s Method for Finding Solitons in Photonic Lattices Raka Jovanović and Milan Tuba Explicit Method for the Numerical Solution of the Fokker-Planck Equation of Filtered Phase Noise Dejan Milić Numerical Method for Computer Study of Liquid Phase Sintering: Densification Due to Gravity-Induced Skeletal Settling Zoran S. Nikolić Computer Algebra and Line Search Predrag Stanimirović, Marko Miladinović and Ivan M. Jovanović Roots of AG-bands Nebojša Stevanović and Petar V. Protić Context Hidden MarkovModel for Named Entity Recognition Branimir T. Todorović, Svetozar R. Rančić, Edin H. Mulalić On the Interpolating Quadratic Spline Zlatko Udovičić Visualization of Infinitesimal Bending of Curves Ljubica S. Velimirović, Svetozar R. Rančić, Milan Lj. Zlatanović

Blurb

Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to the renowned mathematician Gradimir V. Milovanović, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Special features of this volume: - Presents results and approximation methods in various computational settings including polynomial and orthogonal systems, analytic functions, and differential equations. - Provides a historical overview of approximation theory and many of its subdisciplines. - Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences. "Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in engineering and other computational and applied sciences.