Synopses & Reviews
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.
Synopsis
This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanović, represent the recent work of experts in the fields of approximation theory and numerical analysis. The papers describe new trends in this important topic.
Table of Contents
Part I IntroductionThe Scientific Work of Gradimir V. Milovanovi Aleksandar IviMy Collaboration with Gradimir V. Milovanovi Walter GautschiOn Some Major Trends in MathematicsThemistocles M. RassiasPart II Polynomials and Orthogonal SystemsAn Application of Sobolev Orthogonal Polynomials to the Computationof a Special Hankel DeterminantPaul Barry, Predrag M. Rajkovi and Marko D. PetkoviExtremal Problems for Polynomials in the Complex Plane Borislav BojanovEnergy of Graphs and OrthogonalMatrices V. Boin and M. MateljeviInterlacing Property of Zeros of Shifted Jacobi Polynomials Aleksandar S. CvetkoviTrigonometric Orthogonal Systems Aleksandar S. Cvetkovi and Marija P. StaniExperimental Mathematics Involving Orthogonal Polynomials Walter GautschiCompatibility of Continued Fraction Convergents with PadApproximantsJacek Gilewicz and Rados'aw JedynakOrthogonal Decomposition of Fractal Sets Ljubia M. Koci, Sonja Gegovska - Zajkova, Elena BabaePositive Trigonometric Sums and Starlike FunctionsStamatis KoumandosPart III Quadrature FormulaeQuadrature Rules for Unbounded Intervals and Their Application toIntegral EquationsG. Monegato, L. ScuderiGauss-Type Quadrature Formulae for Parabolic Splines withEquidistant KnotsGeno Nikolov and Corina SimianApproximation of the Hilbert Transform on the Real Line Using FreudWeightsIncoronata NotarangeloThe Remainder Term of Gauss-Turan Quadratures for AnalyticFunctions Miodrag M. Spalevi and Miroslav S. PraniTowards a General Error Theory of the Trapezoidal Rule JrgWaldvogelPart IV Differential EquationsFinite Difference Method for a Parabolic Problem with ConcentratedCapacity and Time-Dependent Operator Dejan R. Bojovi and Boko S. JovanoviAdaptive Finite Element Approximation of the Francfort-MarigoModelof Brittle Fracture Siobhan Burke, Christoph Ortner and Endre SüliA NystrmMethod for Solving a Boundary Value Problems on [0, ) Carmelina FrammartinoFinite Difference Approximation of a Hyperbolic Transmission Problem Boko S. JovanoviHomeomorphisms and Fredholm Theory for Perturbations of NonlinearFredholm Maps of Index Zero and of A-Proper Maps with ApplicationsP. S. MilojeviSingular Support and FLq Continuity of Pseudodifferential Operators Stevan Pilipovi, Nenad Teofanov and Joachim ToftOn a Class of Matrix Differential Equations with Polynomial CoefficientsBoro M. PiperevskiPart V ApplicationsOptimized Algorithm for Petviashvili"s Method for Finding Solitons inPhotonic Lattices Raka Jovanovi and Milan TubaExplicit Method for the Numerical Solution of the Fokker-PlanckEquation of Filtered Phase Noise Dejan MiliNumerical Method for Computer Study of Liquid Phase Sintering:Densification Due to Gravity-Induced Skeletal Settling Zoran S. NikoliComputer Algebra and Line Search Predrag Stanimirovi, Marko Miladinovi and Ivan M. JovanoviRoots of AG-bands Neboja Stevanovi and Petar V. ProtiContext Hidden MarkovModel for Named Entity Recognition Branimir T. Todorovi, Svetozar R. Rani, Edin H. MulaliOn the Interpolating Quadratic Spline Zlatko UdoviiVisualization of Infinitesimal Bending of Curves Ljubica S. Velimirovi, Svetozar R. Rani, Milan Lj. Zlatanovi