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. 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 engineering and other computational and applied sciences.

Contenu
Part I Introduction..- The Scientific Work of Gradimir V. Milovanovi (Aleksandar Ivi).- My Collaboration with Gradimir V. Milovanovi (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. Rajkovi and Marko D. Petkovi).- Extremal Problems for Polynomials in the Complex Plane (Borislav Bojanov).- Energy of Graphs and OrthogonalMatrices (V. Boin and M. Mateljevi).- Interlacing Property of Zeros of Shifted Jacobi Polynomials (Aleksandar S. Cvetkovi).- Trigonometric Orthogonal Systems (Aleksandar S. Cvetkovi and Marija P. Stani).- Experimental Mathematics Involving Orthogonal Polynomials (Walter Gautschi).- Compatibility of Continued Fraction Convergents with Padé Approximants (Jacek Gilewicz and Radosaw Jedynak).- Orthogonal Decomposition of Fractal Sets (Ljubia M. Koci, Sonja Gegovska Zajkova, Elena Babae).- 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).- GaussType 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 GaussTur´an Quadratures for Analytic Functions (Miodrag M. Spalevi and Miroslav S. Prani).- Towards a General Error Theory of the Trapezoidal Rule (Jörg Waldvogel).- Part IV Differential Equations.- Finite Difference Method for a Parabolic Problem with Concentrated Capacity and TimeDependent Operator (Dejan R. Bojovi and Boko S. Jovanovi).- Adaptive Finite Element Approximation of the FrancfortMarigo Model of Brittle Fracture (Siobhan Burke, Christoph Ortner andEndre Süli).- A NyströmMethod for Solving a Boundary Value Problems on [0, ) (Carmelina Frammartino).- Finite Difference Approximation of a Hyperbolic Transmission Problem (Boko S. Jovanovi).- Homeomorphisms and Fredholm Theory for Perturbations of Nonlinear Fredholm Maps of Index Zero and of AProper Maps with Applications (P. S. Milojevi).- Singular Support and FLq Continuity of Pseudodifferential Operators (Stevan Pilipovi, 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 Jovanovi and Milan Tuba).- Explicit Method for the Numerical Solution of the FokkerPlanck Equation of Filtered Phase Noise (Dejan Mili).- Numerical Method for Computer Study of Liquid Phase Sintering: Densification Due to GravityInduced Skeletal Settling (Zoran S. Nikoli).- Computer Algebra and Line Search (Predrag Stanimirovi, Marko Miladinovi and Ivan M. Jovanovi).- Roots of AGbands (Neboja Stevanovi and Petar V. Proti).- Context Hidden MarkovModel for Named Entity Recognition (Branimir T. Todorovi, Svetozar R. Rani, Edin H. Mulali).- On the Interpolating Quadratic Spline (Zlatko Udovii).- Visualization of Infinitesimal Bending of Curves (Ljubica S. Velimirovi, Svetozar R. Rani, Milan Lj. Zlatanovi).