Practical extrapolation methods: theory and applications
An important problem that arises in many scientific and engineering applications is that of approximating limits of infinite sequences which in most instances converge very slowly. Thus, to approximate limits with reasonable accuracy, it is necessary to compute a large number of terms, and this is i...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2003
|
| Schriftenreihe: | Cambridge monographs on applied and computational mathematics
10 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | An important problem that arises in many scientific and engineering applications is that of approximating limits of infinite sequences which in most instances converge very slowly. Thus, to approximate limits with reasonable accuracy, it is necessary to compute a large number of terms, and this is in general costly. These limits can be approximated economically and with high accuracy by applying suitable extrapolation (or convergence acceleration) methods to a small number of terms. This state-of-the art reference for mathematicians, scientists and engineers is concerned with the coherent treatment, including derivation, analysis, and applications, of the most useful scalar extrapolation methods. The methods discussed are geared toward common problems in scientific and engineering disciplines. It differs from existing books by concentrateing on the most powerful nonlinear methods, presenting in-depth treatments of them, and showing which methods are most effective for different classes of practical nontrivial problems |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xxii, 519 pages) |
| ISBN: | 9780511546815 |
| DOI: | 10.1017/CBO9780511546815 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043941880 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s2003 |||| o||u| ||||||eng d | ||
| 020 | |a 9780511546815 |c Online |9 978-0-511-54681-5 | ||
| 024 | 7 | |a 10.1017/CBO9780511546815 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9780511546815 | ||
| 035 | |a (OCoLC)992848714 | ||
| 035 | |a (DE-599)BVBBV043941880 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 | ||
| 082 | 0 | |a 511/.42 |2 21 | |
| 084 | |a SK 905 |0 (DE-625)143269: |2 rvk | ||
| 100 | 1 | |a Sidi, Avram |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Practical extrapolation methods |b theory and applications |c Avram Sidi |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2003 | |
| 300 | |a 1 online resource (xxii, 519 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Cambridge monographs on applied and computational mathematics |v 10 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a I. The Richardson extrapolation process and its generalizations -- 1. The Richardson extrapolation process -- 2. Additional topics in Richardson extrapolation -- 3. First generalization of the Richardson extrapolation process -- 4. GREP: Further generalization of the Richardson extrapolation process -- 5. The D-transformation: A GREP for infinite-range integrals -- 6. The d-transformation: A GREP for infinite series and sequences -- 7. Recursive algorithms for GREP -- 8. Analytic study of GREP(¹): Slowly varying ... -- 9. Analytic study of GREP(¹): Quickly varying ... -- 10. Efficient use of GREP(¹): Applications to the ... -- 11. Reduction of the D-transformation for oscillatory infinite-range integrals -- 12. Acceleration of convergence of power series by the d-transformation: Rational d-approximants -- 13. Acceleration of convergence of Fourier and generalized Fourier series by the d-transformation: The complex series approach with APS -- | |
| 505 | 8 | |a 14. Special topics in Richardson extrapolation -- II. Sequence transformations -- 15. The Euler transformation, Aitken [delta]²-process, and Lubkin W-transformation -- 16. The Shanks transformation -- 17. The Padé table -- 18. Generalizations of Padé approximants -- 19. The Levin L- and Sidi S-transformations -- 20. The Wynn and Brezinski algorithms -- 21. The G-transformation and its generalizations -- 22. The transformations of Overholt and Wimp -- 23. Confluent transformations -- 24. Formal theory of sequence transformations -- III. Further applications -- 25. Further applications of extrapolation methods and sequence transformations -- IV. Appendices -- A. Review of basic asymptotics -- B. The Laplace transform and Watson's lemma -- C. The gamma function -- D. Bernoulli numbers and polynomials and the Euler-Maclaurin formula -- E. The Riemann zeta function and the generalized zeta function -- F. Some highlights of polynomial approximation theory -- | |
| 505 | 8 | |a G.A compendium of sequence transformations -- H. Efficient application of sequence transformations: Summary -- I. FORTRAN 77 program for the d(m)-transformation | |
| 520 | |a An important problem that arises in many scientific and engineering applications is that of approximating limits of infinite sequences which in most instances converge very slowly. Thus, to approximate limits with reasonable accuracy, it is necessary to compute a large number of terms, and this is in general costly. These limits can be approximated economically and with high accuracy by applying suitable extrapolation (or convergence acceleration) methods to a small number of terms. This state-of-the art reference for mathematicians, scientists and engineers is concerned with the coherent treatment, including derivation, analysis, and applications, of the most useful scalar extrapolation methods. The methods discussed are geared toward common problems in scientific and engineering disciplines. It differs from existing books by concentrateing on the most powerful nonlinear methods, presenting in-depth treatments of them, and showing which methods are most effective for different classes of practical nontrivial problems | ||
| 650 | 4 | |a Extrapolation | |
| 650 | 0 | 7 | |a Konvergenzbeschleunigung |0 (DE-588)4202431-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Approximation |0 (DE-588)4002498-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Extrapolation |0 (DE-588)4153421-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Extrapolation |0 (DE-588)4153421-9 |D s |
| 689 | 0 | 1 | |a Approximation |0 (DE-588)4002498-2 |D s |
| 689 | 0 | 2 | |a Konvergenzbeschleunigung |0 (DE-588)4202431-6 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-521-66159-1 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9780511546815 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029350850 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511546815 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511546815 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804176884136673280 |
|---|---|
| any_adam_object | |
| author | Sidi, Avram |
| author_facet | Sidi, Avram |
| author_role | aut |
| author_sort | Sidi, Avram |
| author_variant | a s as |
| building | Verbundindex |
| bvnumber | BV043941880 |
| classification_rvk | SK 905 |
| collection | ZDB-20-CBO |
| contents | I. The Richardson extrapolation process and its generalizations -- 1. The Richardson extrapolation process -- 2. Additional topics in Richardson extrapolation -- 3. First generalization of the Richardson extrapolation process -- 4. GREP: Further generalization of the Richardson extrapolation process -- 5. The D-transformation: A GREP for infinite-range integrals -- 6. The d-transformation: A GREP for infinite series and sequences -- 7. Recursive algorithms for GREP -- 8. Analytic study of GREP(¹): Slowly varying ... -- 9. Analytic study of GREP(¹): Quickly varying ... -- 10. Efficient use of GREP(¹): Applications to the ... -- 11. Reduction of the D-transformation for oscillatory infinite-range integrals -- 12. Acceleration of convergence of power series by the d-transformation: Rational d-approximants -- 13. Acceleration of convergence of Fourier and generalized Fourier series by the d-transformation: The complex series approach with APS -- 14. Special topics in Richardson extrapolation -- II. Sequence transformations -- 15. The Euler transformation, Aitken [delta]²-process, and Lubkin W-transformation -- 16. The Shanks transformation -- 17. The Padé table -- 18. Generalizations of Padé approximants -- 19. The Levin L- and Sidi S-transformations -- 20. The Wynn and Brezinski algorithms -- 21. The G-transformation and its generalizations -- 22. The transformations of Overholt and Wimp -- 23. Confluent transformations -- 24. Formal theory of sequence transformations -- III. Further applications -- 25. Further applications of extrapolation methods and sequence transformations -- IV. Appendices -- A. Review of basic asymptotics -- B. The Laplace transform and Watson's lemma -- C. The gamma function -- D. Bernoulli numbers and polynomials and the Euler-Maclaurin formula -- E. The Riemann zeta function and the generalized zeta function -- F. Some highlights of polynomial approximation theory -- G.A compendium of sequence transformations -- H. Efficient application of sequence transformations: Summary -- I. FORTRAN 77 program for the d(m)-transformation |
| ctrlnum | (ZDB-20-CBO)CR9780511546815 (OCoLC)992848714 (DE-599)BVBBV043941880 |
| dewey-full | 511/.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.42 |
| dewey-search | 511/.42 |
| dewey-sort | 3511 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511546815 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05222nmm a2200541zcb4500</leader><controlfield tag="001">BV043941880</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s2003 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511546815</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-511-54681-5</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9780511546815</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9780511546815</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)992848714</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043941880</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511/.42</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 905</subfield><subfield code="0">(DE-625)143269:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Sidi, Avram</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Practical extrapolation methods</subfield><subfield code="b">theory and applications</subfield><subfield code="c">Avram Sidi</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2003</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xxii, 519 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Cambridge monographs on applied and computational mathematics</subfield><subfield code="v">10</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 05 Oct 2015)</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">I. The Richardson extrapolation process and its generalizations -- 1. The Richardson extrapolation process -- 2. Additional topics in Richardson extrapolation -- 3. First generalization of the Richardson extrapolation process -- 4. GREP: Further generalization of the Richardson extrapolation process -- 5. The D-transformation: A GREP for infinite-range integrals -- 6. The d-transformation: A GREP for infinite series and sequences -- 7. Recursive algorithms for GREP -- 8. Analytic study of GREP(¹): Slowly varying ... -- 9. Analytic study of GREP(¹): Quickly varying ... -- 10. Efficient use of GREP(¹): Applications to the ... -- 11. Reduction of the D-transformation for oscillatory infinite-range integrals -- 12. Acceleration of convergence of power series by the d-transformation: Rational d-approximants -- 13. Acceleration of convergence of Fourier and generalized Fourier series by the d-transformation: The complex series approach with APS -- </subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">14. Special topics in Richardson extrapolation -- II. Sequence transformations -- 15. The Euler transformation, Aitken [delta]²-process, and Lubkin W-transformation -- 16. The Shanks transformation -- 17. The Padé table -- 18. Generalizations of Padé approximants -- 19. The Levin L- and Sidi S-transformations -- 20. The Wynn and Brezinski algorithms -- 21. The G-transformation and its generalizations -- 22. The transformations of Overholt and Wimp -- 23. Confluent transformations -- 24. Formal theory of sequence transformations -- III. Further applications -- 25. Further applications of extrapolation methods and sequence transformations -- IV. Appendices -- A. Review of basic asymptotics -- B. The Laplace transform and Watson's lemma -- C. The gamma function -- D. Bernoulli numbers and polynomials and the Euler-Maclaurin formula -- E. The Riemann zeta function and the generalized zeta function -- F. Some highlights of polynomial approximation theory -- </subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">G.A compendium of sequence transformations -- H. Efficient application of sequence transformations: Summary -- I. FORTRAN 77 program for the d(m)-transformation</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">An important problem that arises in many scientific and engineering applications is that of approximating limits of infinite sequences which in most instances converge very slowly. Thus, to approximate limits with reasonable accuracy, it is necessary to compute a large number of terms, and this is in general costly. These limits can be approximated economically and with high accuracy by applying suitable extrapolation (or convergence acceleration) methods to a small number of terms. This state-of-the art reference for mathematicians, scientists and engineers is concerned with the coherent treatment, including derivation, analysis, and applications, of the most useful scalar extrapolation methods. The methods discussed are geared toward common problems in scientific and engineering disciplines. It differs from existing books by concentrateing on the most powerful nonlinear methods, presenting in-depth treatments of them, and showing which methods are most effective for different classes of practical nontrivial problems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Extrapolation</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Konvergenzbeschleunigung</subfield><subfield code="0">(DE-588)4202431-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Approximation</subfield><subfield code="0">(DE-588)4002498-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Extrapolation</subfield><subfield code="0">(DE-588)4153421-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Extrapolation</subfield><subfield code="0">(DE-588)4153421-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Approximation</subfield><subfield code="0">(DE-588)4002498-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Konvergenzbeschleunigung</subfield><subfield code="0">(DE-588)4202431-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-0-521-66159-1</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9780511546815</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029350850</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511546815</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511546815</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043941880 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511546815 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350850 |
| oclc_num | 992848714 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xxii, 519 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge monographs on applied and computational mathematics |
| spelling | Sidi, Avram Verfasser aut Practical extrapolation methods theory and applications Avram Sidi Cambridge Cambridge University Press 2003 1 online resource (xxii, 519 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge monographs on applied and computational mathematics 10 Title from publisher's bibliographic system (viewed on 05 Oct 2015) I. The Richardson extrapolation process and its generalizations -- 1. The Richardson extrapolation process -- 2. Additional topics in Richardson extrapolation -- 3. First generalization of the Richardson extrapolation process -- 4. GREP: Further generalization of the Richardson extrapolation process -- 5. The D-transformation: A GREP for infinite-range integrals -- 6. The d-transformation: A GREP for infinite series and sequences -- 7. Recursive algorithms for GREP -- 8. Analytic study of GREP(¹): Slowly varying ... -- 9. Analytic study of GREP(¹): Quickly varying ... -- 10. Efficient use of GREP(¹): Applications to the ... -- 11. Reduction of the D-transformation for oscillatory infinite-range integrals -- 12. Acceleration of convergence of power series by the d-transformation: Rational d-approximants -- 13. Acceleration of convergence of Fourier and generalized Fourier series by the d-transformation: The complex series approach with APS -- 14. Special topics in Richardson extrapolation -- II. Sequence transformations -- 15. The Euler transformation, Aitken [delta]²-process, and Lubkin W-transformation -- 16. The Shanks transformation -- 17. The Padé table -- 18. Generalizations of Padé approximants -- 19. The Levin L- and Sidi S-transformations -- 20. The Wynn and Brezinski algorithms -- 21. The G-transformation and its generalizations -- 22. The transformations of Overholt and Wimp -- 23. Confluent transformations -- 24. Formal theory of sequence transformations -- III. Further applications -- 25. Further applications of extrapolation methods and sequence transformations -- IV. Appendices -- A. Review of basic asymptotics -- B. The Laplace transform and Watson's lemma -- C. The gamma function -- D. Bernoulli numbers and polynomials and the Euler-Maclaurin formula -- E. The Riemann zeta function and the generalized zeta function -- F. Some highlights of polynomial approximation theory -- G.A compendium of sequence transformations -- H. Efficient application of sequence transformations: Summary -- I. FORTRAN 77 program for the d(m)-transformation An important problem that arises in many scientific and engineering applications is that of approximating limits of infinite sequences which in most instances converge very slowly. Thus, to approximate limits with reasonable accuracy, it is necessary to compute a large number of terms, and this is in general costly. These limits can be approximated economically and with high accuracy by applying suitable extrapolation (or convergence acceleration) methods to a small number of terms. This state-of-the art reference for mathematicians, scientists and engineers is concerned with the coherent treatment, including derivation, analysis, and applications, of the most useful scalar extrapolation methods. The methods discussed are geared toward common problems in scientific and engineering disciplines. It differs from existing books by concentrateing on the most powerful nonlinear methods, presenting in-depth treatments of them, and showing which methods are most effective for different classes of practical nontrivial problems Extrapolation Konvergenzbeschleunigung (DE-588)4202431-6 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Extrapolation (DE-588)4153421-9 gnd rswk-swf Extrapolation (DE-588)4153421-9 s Approximation (DE-588)4002498-2 s Konvergenzbeschleunigung (DE-588)4202431-6 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-66159-1 https://doi.org/10.1017/CBO9780511546815 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sidi, Avram Practical extrapolation methods theory and applications I. The Richardson extrapolation process and its generalizations -- 1. The Richardson extrapolation process -- 2. Additional topics in Richardson extrapolation -- 3. First generalization of the Richardson extrapolation process -- 4. GREP: Further generalization of the Richardson extrapolation process -- 5. The D-transformation: A GREP for infinite-range integrals -- 6. The d-transformation: A GREP for infinite series and sequences -- 7. Recursive algorithms for GREP -- 8. Analytic study of GREP(¹): Slowly varying ... -- 9. Analytic study of GREP(¹): Quickly varying ... -- 10. Efficient use of GREP(¹): Applications to the ... -- 11. Reduction of the D-transformation for oscillatory infinite-range integrals -- 12. Acceleration of convergence of power series by the d-transformation: Rational d-approximants -- 13. Acceleration of convergence of Fourier and generalized Fourier series by the d-transformation: The complex series approach with APS -- 14. Special topics in Richardson extrapolation -- II. Sequence transformations -- 15. The Euler transformation, Aitken [delta]²-process, and Lubkin W-transformation -- 16. The Shanks transformation -- 17. The Padé table -- 18. Generalizations of Padé approximants -- 19. The Levin L- and Sidi S-transformations -- 20. The Wynn and Brezinski algorithms -- 21. The G-transformation and its generalizations -- 22. The transformations of Overholt and Wimp -- 23. Confluent transformations -- 24. Formal theory of sequence transformations -- III. Further applications -- 25. Further applications of extrapolation methods and sequence transformations -- IV. Appendices -- A. Review of basic asymptotics -- B. The Laplace transform and Watson's lemma -- C. The gamma function -- D. Bernoulli numbers and polynomials and the Euler-Maclaurin formula -- E. The Riemann zeta function and the generalized zeta function -- F. Some highlights of polynomial approximation theory -- G.A compendium of sequence transformations -- H. Efficient application of sequence transformations: Summary -- I. FORTRAN 77 program for the d(m)-transformation Extrapolation Konvergenzbeschleunigung (DE-588)4202431-6 gnd Approximation (DE-588)4002498-2 gnd Extrapolation (DE-588)4153421-9 gnd |
| subject_GND | (DE-588)4202431-6 (DE-588)4002498-2 (DE-588)4153421-9 |
| title | Practical extrapolation methods theory and applications |
| title_auth | Practical extrapolation methods theory and applications |
| title_exact_search | Practical extrapolation methods theory and applications |
| title_full | Practical extrapolation methods theory and applications Avram Sidi |
| title_fullStr | Practical extrapolation methods theory and applications Avram Sidi |
| title_full_unstemmed | Practical extrapolation methods theory and applications Avram Sidi |
| title_short | Practical extrapolation methods |
| title_sort | practical extrapolation methods theory and applications |
| title_sub | theory and applications |
| topic | Extrapolation Konvergenzbeschleunigung (DE-588)4202431-6 gnd Approximation (DE-588)4002498-2 gnd Extrapolation (DE-588)4153421-9 gnd |
| topic_facet | Extrapolation Konvergenzbeschleunigung Approximation |
| url | https://doi.org/10.1017/CBO9780511546815 |
| work_keys_str_mv | AT sidiavram practicalextrapolationmethodstheoryandapplications |