North Atlantic Treaty Organization

Approximation Theory, Spline Functions and Applications - NATO Science Series C North Atlantic Treaty Organization 1992 edition

Marc Notes: Includes bibliographical references and index.; Published in cooperation with NATO Scientific Affairs Division.; Proceedings of the NATO Advanced Study Institute on Approximation Theory, Spline Functions and Applications, Maratea, Italy, April 28-May 9, 1991--T.p. verso. Table of Contents: Preface. Approximation by Functions of Nonclassical Form; E. W. Cheney. Wavelets- with Emphasis on Spline-Wavelets and Applications to Signal Analysis; C. K. Chui. Pade Approximation in One and More Variables; A. Cuyt. Rational Hermite Interpolation in One and More Variables; A. Cuyt. The Method of Alternating Orthogonal Projections; F. Deutsch. Selections for Metric Projections; F. Deutsch. Weighted Polynomials; M. v. Golitschek. Some Aspects of Radial Basis Function Approximation; W. A. Light. Using the Refinement Equation for the Construction of Pre-Wavelets VI: Shift Invariant Subspaces; C. A. Micchelli. A Tutorial on Multivariate Wavelet Decomposition; C. A. Micchelli. Error Estimates for Near-Minimax Approximations; G. M. Phillips. Different Metrics and Location Problems; E. Casini, P. L. Papini. On the Effectiveness of Some Inversion Methods for Noisy Fourier Series; L. De Michele, M. Di Natale, D. Roux. A Generalization of N-Widths; A. G. Aksoy. The Equivalence of the Usual and Quotient Topologies for CINFINITY(E) when E sub Rn is Whitney p-Regular; L. P. Bos, P. D. Milman. Korovkin Theorems for Vector-Valued Continuous Functions; M. Campiti. On Modified Bojanic-Shisha Operators; A. S. Cavaretta, S. S. Guo. A Property of Zeros and Cotes Numbers of Hermite and Laguerre Orthogonal Polynomials; F. Costabile. Hermite-Fejer and Hermite Interpolation; G. Criscuolo, B. Della Vecchia, G. Mastroianni. New Results on Lagrange Interpolation; G. Criscuolo, G. Mastroianni. Ambiguous Loci in Best Approximation Theory; F. S. De Blasi, J. Myjak. A Theorem on Best Approximations in Topological Vector Spaces; E. De Pascale, G. Trombetta. On theCharacterization of Totally Positive Matrices; M. Gasca, J. M. Pena. Iterative Methods for the General Order Complementarity Problem; G. Isac. Wavelets, Splines, and Divergence-Free Vector Functions; P-G. Lemarie-Rieusset. An Approach to Meromorphic Approximation in a Stein Manifold; C. H. Lutterodt. Approximating Fixed Points for Nonexpansive Maps in Hilbert Spaces; G. Marino. On Approximation and Interpolation of Convex Functions; M. Neamtu. Convergence of Approximating Fixed Point Sets for Multivalued Nonexpansive Mappings; P. Pietramala. A Subdivision Algorithm for Non-Uniform B-Splines; R. Qu, J. A. Gregory. Some Applications of an Approximation Theorem for Fixed Points of Multi-Valued Contractions; B. Ricceri. Geometrical Differentiation and High-Accuracy Curve Interpolation; R. Schaback. On Best Simultaneous Approximation in Normed Linear Spaces; V. M. Sehgal, S. P. Singh. Some Examples Concerning Projection Constants; B. Shekhtman. Subject Index."Publisher Marketing: This volume containing the proceedings of the NATO Advanced Study Institute embodies survey articles and recent results from the theory of splines, spline-wavelets, multivariate wavelet decomposition, interpolation theory, polynomical approximation, near-minimax approximations, rational interpolants, and Pade approximants in one and several variables, radial basis approximation, optimixation theory, orthogonal polynomials, and more.

Contributor Bio:  North Atlantic Treaty Organization Dedication. Preface. Acknowledgments. Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries.- Geometric algebra Projective Geometries; Affine and other geometries; Affine Geometry of pseudo-euclidean space; Conformal Geometry and the Horosphere; References. Content-Based Information Retrieval by Group Theoretical Methods.- Introduction; Motivating Examples; General Concept; Fault Tolerance.- Applications, Prototypes, and Test Results; Related Work and Future Research; References.- Four Problems in Radar.-Introduction; Radar Fundamentals; Radar Waveforms; Signal Processing; Space-Time Adaptive Processing; Four Problems in Radar; Conclusions. Introduction to Generalized Classical and Quantum Signal and System Theories on Groups and Hypergroups.-Generalized classical signal/system theory on hypergroups; Generalized quantum signal/system theory on hypergroups; Conclusion; References. Lie Groups and Lie Algebras in Robotics.- Introduction -- Rigid Body Motions; Lie Groups; Finite Screw Motions; Mechanical Joints; Invisible Motion and Gripping; Forward Kinematics; Lie Algebra; The Adjoint Representation; The Exponential Map Derivatives of Exponentials; Jacobians; Concluding Remarks; References. Quantum/Classical Interface: a Geometric Approach from the Classical Side.- Introduction Paravector Space as Spacetime; Eigenspinors; Spin; Dirac Equation; Bell's Theorem; Qubits and Entanglement; Conclusions; References. PONS, Reed-Muller Codes, and Group Algebras.- Introduction; Analytic Theory of One-Dimensional PONS (Welti); Shapiro Sequences, Reed-Muller Codes, and Functional Equations; Group Algebras; Reformulation of Classical PONS; Group Algebra of Classical PONS; GroupAlgebra Convolution; Splitting Sequences; Historical Appendix on PONS; References. Clifford Algebras as a Unified Language.- Introduction; Clifford algebras as models of physical spaces; Clifford Algebras as Models of Perceptual Multicolor Spaces; Hypercomplex-Valued invariants of nD multicolor images; Conclusions; Acknowledgments; References. Recent Progress and Applications in Group FFTs.-Introduction; Finite group FFTs; FFTs for compact groups; Noncompact groups; References. Group Filters and Image Processing.- Introduction: Classical Digital Signal Processing; Abelian Group DSP; Nonabelian Groups; Examples; Group Transforms; Group Filters; Line-like Images; Acknowledgments; References. A Geometric Algebra Approach to Some Problems of Robot Vision.- Introduction; Local Analysis of Multi-dimensional Signals; Knowledge Based Neural Computing; Acknowledgments; References. Group Theory in Radar and Signal Processing.- Introduction; How a Radar Works; Representations; Representations and Radar; Ambiguity Functions; The Wide Band Case; References. Geometry of Paravector Space with Applications to Relativistic Physics.- Clifford Algebras in Physics; Paravector Space as Spacetime; Interpretation; Eigenspinors; Maxwell's Equation; Conclusions; References. A Unified Approach to Fourier-Clifford-Prometheus Transforms- Introduction; New construction of classical and multiparametric Prometheus transforms; PONS associated with Abelian groups; Fast Fourier-Prometheus Transforms; Conclusions; Acknowledgments; References. Fast Color Wavelet Transforms.- Introduction; Color images; Color Wavelet-Haar-Prometheus transforms; Edge detection and compression of color images; Conclusion; Acknowledgments; References. Selected Problems; Various Authors.- Transformations of Euclidean Space and Clifford Geometric; Algebra; References; On the Distribution of Kloosterman Sums on Polynomials over Quaternions; References; Harmonic Sliding Analysis Problems; References; Spectral Analysis under Conditions of Uncertainty; A Canonical Basis for Maximal Tori of the Reductive Centrizer of a Nilpotent Element; References; 6 The Quantum Chaos Conjecture References; Four Problems in Radar; Topic Index; Author Index