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. Milovanovi¿, 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.

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. Božin 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 Rados¿aw Jedynak
Orthogonal Decomposition of Fractal Sets
Ljubiša M. Koci¿, Sonja Gegovska - Zajkova, Elena Babäe
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. Spalevi¿ and Miroslav S. Prani¿
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. Bojovi¿ and Boško S. Jovanovi¿
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. Jovanovi¿
Homeomorphisms and Fredholm Theory for Perturbations of Nonlinear
Fredholm Maps of Index Zero and of A-Proper 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 Fokker-Planck
Equation of Filtered Phase Noise
Dejan Mili¿
Numerical Method for Computer Study of Liquid Phase Sintering:
Densification Due to Gravity-Induced Skeletal Settling
Zoran S. Nikoli¿
Computer Algebra and Line Search
Predrag Stanimirovi¿, Marko Miladinovi¿ and Ivan M. Jovanovi¿
Roots of AG-bands
Nebojša Stevanovi¿ and Petar V. Proti¿
Context Hidden MarkovModel for Named Entity Recognition
Branimir T. Todorovi¿, Svetozar R. Ran¿i¿, Edin H. Mulali¿
On the Interpolating Quadratic Spline
Zlatko Udovi¿i¿
Visualization of Infinitesimal Bending of Curves
Ljubica S. Velimirovi¿, Svetozar R. Ran¿i¿, Milan Lj. Zlatanovi¿