Includes results from diverse areas of mathematics, engineering and the computational sciences
Presents 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 subdiciplines
Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences
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.
Part I IntroductionThe Scientific Work of Gradimir V. Milovanovic Aleksandar IvicMy Collaboration with Gradimir V. Milovanovic 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. Rajkovic and Marko D. PetkovicExtremal Problems for Polynomials in the Complex Plane Borislav BojanovEnergy of Graphs and OrthogonalMatrices V. Božin and M. MateljevicInterlacing Property of Zeros of Shifted Jacobi Polynomials Aleksandar S. CvetkovicTrigonometric Orthogonal Systems Aleksandar S. Cvetkovic and Marija P. StanicExperimental Mathematics Involving Orthogonal Polynomials Walter GautschiCompatibility of Continued Fraction Convergents with PadéApproximantsJacek Gilewicz and Radoslaw JedynakOrthogonal Decomposition of Fractal Sets Ljubiša M. Kocic, Sonja Gegovska - Zajkova, Elena BabacePositive 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-Tur´an Quadratures for AnalyticFunctions Miodrag M. Spalevic and Miroslav S. PranicTowards a General Error Theory of the Trapezoidal Rule JörgWaldvogelPart IV Differential EquationsFinite Difference Method for a Parabolic Problem with ConcentratedCapacity and Time-Dependent Operator Dejan R. Bojovic and Boško S. JovanovicAdaptive Finite Element Approximation of the Francfort-MarigoModelof Brittle Fracture Siobhan Burke, Christoph Ortner and Endre SüliA NyströmMethod for Solving a Boundary Value Problems on [0, ) Carmelina FrammartinoFinite Difference Approximation of a Hyperbolic Transmission Problem Boško S. JovanovicHomeomorphisms and Fredholm Theory for Perturbations of NonlinearFredholm Maps of Index Zero and of A-Proper Maps with ApplicationsP. S. MilojevicSingular Support and FLq Continuity of Pseudodifferential Operators Stevan Pilipovic, 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 Jovanovic and Milan TubaExplicit Method for the Numerical Solution of the Fokker-PlanckEquation of Filtered Phase Noise Dejan MilicNumerical Method for Computer Study of Liquid Phase Sintering:Densification Due to Gravity-Induced Skeletal Settling Zoran S. NikolicComputer Algebra and Line Search Predrag Stanimirovic, Marko Miladinovic and Ivan M. JovanovicRoots of AG-bands Nebojša Stevanovic and Petar V. ProticContext Hidden MarkovModel for Named Entity Recognition Branimir T. Todorovic, Svetozar R. Rancic, Edin H. MulalicOn the Interpolating Quadratic Spline Zlatko UdovicicVisualization of Infinitesimal Bending of Curves Ljubica S. Velimirovic, Svetozar R. Rancic, Milan Lj. Zlatanovic
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.
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. The papers describe new trends in this important topic.
Part I Introduction..- The Scientific Work of Gradimir V. Milovanovic (Aleksandar Ivic).- My Collaboration with Gradimir V. Milovanovic (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. Rajkovic and Marko D. Petkovic).- Extremal Problems for Polynomials in the Complex Plane (Borislav Bojanov).- Energy of Graphs and OrthogonalMatrices (V. Bozin and M. Mateljevic).- Interlacing Property of Zeros of Shifted Jacobi Polynomials (Aleksandar S. Cvetkovic).- Trigonometric Orthogonal Systems (Aleksandar S. Cvetkovic and Marija P. Stanic).- Experimental Mathematics Involving Orthogonal Polynomials (Walter Gautschi).- Compatibility of Continued Fraction Convergents with Padé Approximants (Jacek Gilewicz and Radoslaw Jedynak).- Orthogonal Decomposition of Fractal Sets (Ljubisa M. Kocic, Sonja Gegovska Zajkova, Elena Babace).- 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. Spalevic and Miroslav S. Pranic).- 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. Bojovic and Bosko S. Jovanovic).- 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 (Bosko S. Jovanovic).- Homeomorphisms and Fredholm Theory for Perturbations of Nonlinear Fredholm Maps of Index Zero and of AProper Maps with Applications (P. S. Milojevic).- Singular Support and FLq Continuity of Pseudodifferential Operators (Stevan Pilipovic, 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 Jovanovic and Milan Tuba).- Explicit Method for the Numerical Solution of the FokkerPlanck Equation of Filtered Phase Noise (Dejan Milic).- Numerical Method for Computer Study of Liquid Phase Sintering: Densification Due to GravityInduced Skeletal Settling (Zoran S. Nikolic).- Computer Algebra and Line Search (Predrag Stanimirovic, Marko Miladinovic and Ivan M. Jovanovic).- Roots of AGbands (Nebojsa Stevanovic and Petar V. Protic).- Context Hidden MarkovModel for Named Entity Recognition (Branimir T. Todorovic, Svetozar R. Rancic, Edin H. Mulalic).- On the Interpolating Quadratic Spline (Zlatko Udovicic).- Visualization of Infinitesimal Bending of Curves (Ljubica S. Velimirovic, Svetozar R. Rancic, Milan Lj. Zlatanovic).
Inhaltsverzeichnis
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¿
Klappentext
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.
Includes results from diverse areas of mathematics, engineering and the computational sciences
Presents 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 subdiciplines
Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences
