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1. |
Record Nr. |
UNINA9910783009603321 |
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Autore |
Buhmann M. D (Martin Dietrich), <1963-> |
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Titolo |
Radial basis functions : theory and implementations / / Martin Buhmann [[electronic resource]] |
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Pubbl/distr/stampa |
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Cambridge : , : Cambridge University Press, , 2003 |
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ISBN |
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1-107-12800-5 |
1-280-43229-2 |
9786610432295 |
0-511-17904-9 |
0-511-04020-2 |
0-511-14894-1 |
0-511-32602-5 |
0-511-54324-7 |
0-511-05124-7 |
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Descrizione fisica |
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1 online resource (x, 259 pages) : digital, PDF file(s) |
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Collana |
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Cambridge monographs on applied and computational mathematics ; ; 12 |
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Disciplina |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
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Nota di bibliografia |
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Includes bibliographical references (p. 246-257) and index. |
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Nota di contenuto |
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1. Introduction -- 1.1 Radial basis functions -- 1.2 Applications -- 1.3 Contents of the book -- 2. Summary of methods and applications -- 2.1 Invertibility of interpolation matrices -- 2.2 Convergence analysis -- 2.3 Interpolation and convergence -- 2.4 Applications to PDEs -- 3. General methods for approximation and interpolation -- 3.1 Polynomial schemes -- 3.2 Piecewise polynomials -- 3.3 General nonpolynomial methods -- 4. Radial basis function approximation on infinite grids -- 4.1 Existence of interpolants -- 4.2 Convergence analysis -- 4.3 Numerical properties of the interpolation linear system -- 4.4 Convergence with respect to parameters in the radial functions -- 5. Radial basis functions on scattered data -- 5.1 Nonsingularity of interpolation matrices -- 5.2 Convergence analysis -- 5.3 Norm estimates and condition numbers of interpolation matrices -- 6. Radial basis functions with compact support -- 6.1 Introduction -- 6.2 |
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Wendland's functions -- 6.3 Another class of radial basis functions with compact support -- 6.4 Convergence -- 6.5 A unified class -- 7. Implementations -- 7.1 Introduction -- 7.2 The BFGP algorithm and the new Krylov method -- 7.3 The fast multipole algorithm -- 7.4 Preconditioning techniques -- 8. Least squares methods -- 8.1 Introduction to least squares -- 8.2 Approximation order results -- 8.3 Discrete least squares -- 8.4 Implementations -- 8.5 Neural network applications -- 9. Wavelet methods with radial basis functions -- 9.1 Introduction to wavelets and prewavelets -- 9.2 Basic definitions and constructions -- 9.3 Multiresolution analysis and refinement -- 9.4 Special constructions -- 10. Further results and open problems -- 10.1 Further results -- 10.2 Open problems -- Appendix: Some essentials on Fourier transforms. |
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Sommario/riassunto |
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In many areas of mathematics, science and engineering, from computer graphics to inverse methods to signal processing, it is necessary to estimate parameters, usually multidimensional, by approximation and interpolation. Radial basis functions are a powerful tool which work well in very general circumstances and so are becoming of widespread use as the limitations of other methods, such as least squares, polynomial interpolation or wavelet-based, become apparent. The author's aim is to give a thorough treatment from both the theoretical and practical implementation viewpoints. For example, he emphasises the many positive features of radial basis functions such as the unique solvability of the interpolation problem, the computation of interpolants, their smoothness and convergence and provides a careful classification of the radial basis functions into types that have different convergence. A comprehensive bibliography rounds off what will prove a very valuable work. |
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2. |
Record Nr. |
UNIORUON00083217 |
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Autore |
HEUSCH, Luc : de |
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Titolo |
Le roi de Kongo et les monstres sacrés : mythes et rites bantous III / Luc de Heusch |
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Pubbl/distr/stampa |
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[Paris], : Gallimard, c2000 |
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ISBN |
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Descrizione fisica |
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424 p., [4] p. di tav. ; 21 cm |
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Disciplina |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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3. |
Record Nr. |
UNINA9911019084903321 |
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Autore |
Brown D. J |
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Titolo |
Fused pyrimidines . Part three Pteridines / / D.J. Brown |
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Pubbl/distr/stampa |
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New York, : Wiley & Sons, c1988 |
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ISBN |
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1-282-30165-9 |
9786612301650 |
0-470-18689-5 |
0-470-18837-5 |
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Descrizione fisica |
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1 online resource (762 p.) |
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Collana |
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Chemistry of heterocyclic compounds ; ; 24/3 |
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Disciplina |
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547.593 |
547/.59/05 |
547/.593 |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliography and index. |
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Nota di contenuto |
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FUSED PYRIMIDINES; Contents; List of Tables; CHAPTER I. INTRODUCTION TO THE PTERIDINES; 1. History; 2. Nomenclature; 3. The Basis of Pteridine Chemistry; 4. A General Summary of Pteridine Chemistry; A. Electrophilic Reactions; B. Direct Nucleophilic Substitutions; C. Nucleophilic Metatheses; (1) Replacement of Halogeno Substituents; (a) By Amino or Substituted-Amino Groups; (b) By Hydroxy-Oxo Substituents; (c) By Alkoxy or Aryloxy Groups; (d) By Mercapto- Thioxo Substituents; (e) By Alkylthio or Arylthio Groups; (f) By Sulfo Groups; (g) By Other Groups; (2) Replacement of Alkoxy Groups |
(3) Replacement of Alkylthio Groups(4) Replacement of Sulfo Groups; (5) Replacement of Alkylsulfonyl Groups; D. Other Metatheses; (1) Pteridinones to Chloropteridines; (2) Pteridinones to Pteridinethiones; (3) Pteridinethiones to Pteridinones; (4) Pteridinones to Pteridinamines; (5) Pteridinethiones to Pteridinamines or Pteridinimines; (6) Pteridinamines or Pteridinimines to Pteridinones; E. Addition Reactions; (1) Covalent Hydration and Similar Additions; (2) Addition of Phenyllithium; F. Oxidative Reactions; (1) Nuclear Oxidation; (2) Formation of N-Oxides |
(3) Oxidative Modification of Groups(a) C- Methyl to C-Formyl; (b) C-Alkyl to C-Acyl; (c) Alkyl to Carboxy; (d) Hydroxyalkyl to Formyl; (e) Hydroxyalkyl to Carboxy; (f) C-Formyl to Carboxy; (g) C-Acyl to Carboxy; (h) Pteridinethiones to Dipteridinyl Disulfides; (i) Thioxo to Sulfeno, Sulfino, or Sulfo; (j) Alkylthio to Alkylsulfinyl or Alkylsulfonyl; G. Reductive Reactions; (1) Nuclear Reduction; (2) Reductive Removal of Groups; (3) Reductive Modification of Groups; (a) C-Formyl to Hydroxymethyl; (b) Carboxy or Alkoxycarbonyl to Hydroxymethyl; (c) C-Acyl to Hydroxyalkyl or Alkyl |
(d) Cyano to Aminomethyl(e) Sulfo, Sulfino, or Sulfeno to Thioxo; H. Other Substituent Modifications; (1) Modification of Alkyl Groups; (2) Modification of Oxo Substituents; (3) Modification of Thioxo Substituents; (4) Modification of Amino Groups; (a) Amino to Acylamino; (b) Amino to Alkylideneamino; (c) Amino to Alkylamino; (d) Transamination; (5) Modification of Carboxy and Related Groups; (a) Carboxy to Related Groups; (b) Alkoxycarbonyl to Related Groups; (c) Carbamoyl to Related Groups; (d) Cyano to Related Groups; (e) C-Formyl to Related Groups; (f) C-Acyl to Related Groups |
I. DecarboxylationJ. Homolytic C-Acylation; K. Degradation to Pyrazines or Pyrimidines; (1) Degradation of Pteridine; (2) Degradation of Pteridinones; (3) Degradation of Pteridinamines and Pteridinimines; (4) Degradation of Pteridine N-Oxides; 5. Physical Properties of Pteridines; CHAPTER II. PRIMARY SYNTHESES FROM PYRIMIDINES; 1. The Gabriel and Colman Synthesis from 4,5- Pyrimidinediamines and α-Dicarbonyl Compounds; A. Use of the α-Dialdehyde, Glyoxal; B. Use of α-Aldehydoketones; (1) Simple Cases; (2) Cases with One Functional Group; (3) Cases with Two Functional Groups |
(a) The 6- or 7-Alkyl-2-amino-4(3H)-pteridinones |
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Sommario/riassunto |
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Introduction to the Pteridines. Primary Syntheses from Pyrimidines. Primary Syntheses from Pyrazines or Other Heterocycles. Pteridine and Its Alkyl and Aryl Derivatives. Halogenopteridines. Tautomeric Pteridinones and Extranuclear Hydroxypteridines. Aloxypteridines, N-alkylpteridines, and Pteridine N-oxides. The Sulfur-containing Pteridines. Pteridine Amines and Imines. Pteridinecarboxylic Acids and Related Compounds. The Hydropteridines. Ionization and Spectra. Table of Simple Pteridines. References. Index. |
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