Handbook of Analytic Computational Methods in Applied Mathematics

Working computationally in applied mathematics is the very essence of dealing with real-world problems in science and engineering. Approximation theory-on the borderline between pure and applied mathematics- has always supplied some of the most innovative ideas, computational methods, and original approaches to many types of problems. The first of its kind, the Handbook on Analytic-Computational Methods in Applied Mathematics comprises 22 self-contained chapters focused on various aspects of analytic computational methods in approximation theory and other related fields. The articles represent the leading research activities of contemporary, mainstream applied mathematics and address problems in a broad range of disciplines, from economics to statistics, dynamic programming, and engineering.

Degree of Approximation of Order Statistics Functionals, Dependent Case, G.A. Anastassiou Regularization and Stabilization of Inverse Problems, C.W. GroetschTrapezoidal Type Rules from an Inequalities Point of View, P. Cerone and S.S. DragomirMidpoint Type Rules from an Inequalities Point of View, P. Cerone and S.S. DragomirA Unified Approach for Solving Equations, Part I: On Infinite Dimensional Spaces, I.K. ArgyrosA Unified Approach for Solving Equations, Part II: On Finite Dimensional Spaces, I.K. ArgyrosUniqueness for Spherically Convergent Multiple Trigonometric Series, J.M. AshRoundoff Error Analysis for Fast Trigonometric Transforms, M. Tasche anfd H. ZeunerBiorthogonal Local Trigonometric Bases, K. BittnerPólya-Type Inequalities, C.E. Pearce, J. Pecaric, and S. VarosanecLimit Theorems and Best Constants in Approximation Theory. Approximation Theory in Random Setting, M.I. GanzburgApproximation Theory in Fuzzy Setting, S.G. GalGlobal Smoothness Preservation by Multivariate Bernstein-Type Operators, J. de la Cal and A.M. ValleSummation Kernels for Orthogonal Polynomial Systems, F. Filbir, R. Lasser, and J. ObermaierDigitized PDE Method for Data Restoration, S. Osher and J. ShenBoundary Quadrature Formulas and Their Application, T.-X. HeValue at Risk: Recent Advances, I.M. Khindanova and S. RachevAsset and Liability Management: Recent Advances, S. Rachev and Y. TokatOptimization Problems in Fair Division Theory, M. Dall'AglioBinomial-Type Coefficients and Classical Approximation Processes, M. CampitiOn Scattered Data Representations Using Bivariate Splines, D. Hong