Orthogonal polynomials: computation and approximation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford Univ. Pr.
2004
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Numerical mathematics and scientific computation
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 301 S. |
| ISBN: | 0198506724 |
Internformat
MARC
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| 245 | 1 | 0 | |a Orthogonal polynomials |b computation and approximation |c Walter Gautschi |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford |b Oxford Univ. Pr. |c 2004 | |
| 300 | |a VII, 301 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Numerical mathematics and scientific computation | |
| 650 | 7 | |a Orthogonale reeksen |2 gtt | |
| 650 | 4 | |a Polynômes orthogonaux | |
| 650 | 4 | |a Orthogonal polynomials | |
| 650 | 0 | 7 | |a Orthogonale Polynome |0 (DE-588)4172863-4 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804132894372790272 |
|---|---|
| adam_text | CONTENTS
Preface
Basic
Theory
1.1 Orthogonal
polynomials
1.1.1 Definition
and existence
1.1.2
Examples
1.2
Properties of orthogonal polynomials
1.2.1
Symmetry
1.2.2
Zeros
1.2.3
Discrete orthogonality
1.2.4
Extremal properties
1.3
Three-term recurrence relation
1.3.1
Monic orthogonal polynomials
1.3.2
Orthonormal
polynomials
1.3.3
Christoffel-Darboux formulae
1.3.4
Continued fractions
1.3.5
The recurrence relation outside the support
interval
1.4
Quadrature rules
1.4.1
Interpolatory
quadrature rules and beyond
1.4.2
Gauss-type quadrature rules
1.5
Classical orthogonal polynomials
1.5.1
Classical orthogonal polynomials of a
continuous variable
1.5.2
Classical orthogonal polynomials of a
discrete variable
1.6
Kernel polynomials
1.6.1
Existence and elementary properties
1.6.2
Recurrence relation
1.7
Sobolev orthogonal polynomials
1.7.1
Definition and properties
1.7.2
Recurrence relation and zeros
1.8
Orthogonal polynomials on the semicircle
1.8.1
Definition, existence, and representation
1.8.2
Recurrence relation
1.8.3
Zeros
1.9
Notes to Chapter
1
Computational Methods
2.1
Moment-based methods
2.1.1
Classical approach via moment determinants
2.1.2
Condition of nonlinear maps
2.1.3
The moment maps Gn and Kn
2.1
A Condition of Gn
:
μ
(->
η
2.1.5
Condition of Gn
:
m
ι—
>
-f
2.1.6
Condition of
К
n
:
m *-^> p
2.1
Л
Modified Chebyshev algorithm
2.1.8
Finite expansions in orthogonal polynomials
2.1.9
Examples
2.2
Discretization methods
2.2.1
Convergence of discrete orthogonal polynomials
to continuous ones
2.2.2
A general-purpose discretization procedure
2.2.3
Computing the recursion coefficients of a
discrete measure
2.2.4
A multiple-component discretization method
2.2.5
Examples
2.2.6
Discretized modified Chebyshev algorithm
2.3
Computing Cauchy integrals of orthogonal
polynomials
2.3.1
Characterization in terms of minimal solutions
2.3.2
A continued fraction algorithm
2.3.3
Examples
2.4
Modification algorithms
2.4.1 Christoffel
and generalized
Christoffel
theorems
2.4.2
Linear factors
2.4.3
Quadratic factors
2.4.4
Linear divisors
2.4.5
Quadratic divisors
2.4.6
Examples
2.5
Computing Sobolev orthogonal polynomials
2.5.1
Algorithm based on moment information
2.5.2
Stieltjes-type algorithm
2.5.3
Zeros
2.5.4
Finite expansions in Sobolev orthogonal
polynomials
2.6
Notes to Chapter
2
Applications
3.1
Quadrature
3.1.1
Computation of Gauss-type quadrature
formulae
3.1.2 Gauss-Kronrod
quadrature
formulae and their
computation
3.1.3
Gauss-Turán
quadrature formulae and their
computation
3.1.4
Quadrature formulae based on rational
functions
3.1.5
Cauchy principal value integrals
3.1.6
Polynomials orthogonal on several intervals
3.1.7
Quadrature estimation of matrix
funcţionale
3.2
Least squares approximation
3.2.1
Classical least squares approximation
3.2.2
Constrained least squares approximation
3.2.3
Least squares approximation in Sobolev spaces
3.3
Moment-preserving spline approximation
3.3.1
Approximation on the positive real line
3.3.2
Approximation on a compact interval
3.4
Slowly convergent series
3.4.1
Series generated by a Laplace transform
3.4.2
Alternating series generated by a Laplace
transform
3.4.3
Series generated by the derivative of a Laplace
transform
3.4.4
Alternating series generated by the derivative
of a Laplace transform
3.4.5
Slowly convergent series occurring in plate
contact problems
3.5
Notes to Chapter
3
Bibliography
Index
|
| any_adam_object | 1 |
| author | Gautschi, Walter 1927- |
| author_GND | (DE-588)119264315 |
| author_facet | Gautschi, Walter 1927- |
| author_role | aut |
| author_sort | Gautschi, Walter 1927- |
| author_variant | w g wg |
| building | Verbundindex |
| bvnumber | BV019428127 |
| callnumber-first | Q - Science |
| callnumber-label | QA404 |
| callnumber-raw | QA404.5 |
| callnumber-search | QA404.5 |
| callnumber-sort | QA 3404.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 905 |
| classification_tum | MAT 412f |
| ctrlnum | (OCoLC)55622265 (DE-599)BVBBV019428127 |
| dewey-full | 515/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.55 |
| dewey-search | 515/.55 |
| dewey-sort | 3515 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV019428127 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:00:04Z |
| institution | BVB |
| isbn | 0198506724 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012888157 |
| oclc_num | 55622265 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-739 DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-739 DE-11 |
| physical | VII, 301 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Oxford Univ. Pr. |
| record_format | marc |
| series2 | Numerical mathematics and scientific computation |
| spelling | Gautschi, Walter 1927- Verfasser (DE-588)119264315 aut Orthogonal polynomials computation and approximation Walter Gautschi 1. publ. Oxford Oxford Univ. Pr. 2004 VII, 301 S. txt rdacontent n rdamedia nc rdacarrier Numerical mathematics and scientific computation Orthogonale reeksen gtt Polynômes orthogonaux Orthogonal polynomials Orthogonale Polynome (DE-588)4172863-4 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Orthogonale Polynome (DE-588)4172863-4 s Approximation (DE-588)4002498-2 s DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012888157&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gautschi, Walter 1927- Orthogonal polynomials computation and approximation Orthogonale reeksen gtt Polynômes orthogonaux Orthogonal polynomials Orthogonale Polynome (DE-588)4172863-4 gnd Approximation (DE-588)4002498-2 gnd |
| subject_GND | (DE-588)4172863-4 (DE-588)4002498-2 |
| title | Orthogonal polynomials computation and approximation |
| title_auth | Orthogonal polynomials computation and approximation |
| title_exact_search | Orthogonal polynomials computation and approximation |
| title_full | Orthogonal polynomials computation and approximation Walter Gautschi |
| title_fullStr | Orthogonal polynomials computation and approximation Walter Gautschi |
| title_full_unstemmed | Orthogonal polynomials computation and approximation Walter Gautschi |
| title_short | Orthogonal polynomials |
| title_sort | orthogonal polynomials computation and approximation |
| title_sub | computation and approximation |
| topic | Orthogonale reeksen gtt Polynômes orthogonaux Orthogonal polynomials Orthogonale Polynome (DE-588)4172863-4 gnd Approximation (DE-588)4002498-2 gnd |
| topic_facet | Orthogonale reeksen Polynômes orthogonaux Orthogonal polynomials Orthogonale Polynome Approximation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012888157&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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