skip to content
Laurent series and their Padé approximations Preview this item
ClosePreview this item
Checking...

Laurent series and their Padé approximations

Author: Adhemar Bultheel
Publisher: Basel ; Boston : Birkhäuser Verlag, 1987.
Series: Operator theory, advances and applications, v. 27.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy online

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Additional Physical Format: Online version:
Bultheel, Adhemar.
Laurent series and their Padé approximations.
Basel ; Boston : Birkhäuser Verlag, 1987
(OCoLC)623756191
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Adhemar Bultheel
ISBN: 3764319402 9783764319403 0817619402 9780817619404
OCLC Number: 16647917
Description: xi, 274 pages : illustrations ; 24 cm.
Contents: 2. Introduction.- 2.1 Classical Pade approximation.- 2.2 Toeplitz and Hankel systems.- 2.3 Continued fractions.- 2.4 Orthogonal polynomials.- 2.5 Rhombus algorithms and convergence.- 2.6 Block structure.- 2.7 Laurent-Pade approximants.- 2.8 The projection method.- 2.9 Applications.- 2.10 Outline.- 3. Moebius transforms, continued fractions and Pade approximants.- 3.1 Moebius transforms.- 3.2 Flow graphs.- 3.3 Continued fractions (CF).- 3.4 Formal series.- 3.5 Pade approximants.- 4. Two algorithms.- 4.1 Algorithm 1.- 4.2 Algorithm 2.- 5. All kinds of Pade Approximants.- 5.1 Pade approximants.- 5.2 Laurent-Pade approximants.- 5.3 Two-point Pade approximants.- 6. Continued fractions.- 6.1 General observations.- 6.2 Some special cases.- 7. Moebius transforms.- 7.1 General observations.- 7.2 Some special cases.- 8. Rhombus algorithms.- 8.1 The ab parameters (sawtooth path).- 8.2. The FG parameters (row path).- 8.3. A staircase path.- 8.4 ?? paramaters (diagonal path).- 8.5 Some dual results.- 8.6 Relation with classical algorithms.- 9. Biorthogonal polynomials, quadrature and reproducing kernels.- 9.1 Biorthogonal polynomials.- 9.2 Interpolatory quadrature methods.- 9.3 Reproducing kernels.- 9.4 Other orthogonality relations.- 10. Determinant expressions and matrix interpretations.- 10.1 Determinant expressions.- 10.2 Matrix interpretations.- 10.2.1 Toeplitz matrices.- 10.2.2 Hankel matrices.- 10.2.3 Tridiagonal matrices.- 11. Symmetry Properties.- 11.1 Symmetry for F(z) and $$\hat F$$(z) = F(1/z).- 11.2 Symmetry for F(z) and G(z) = 1/F(z).- 12. Block structures.- 12.1 Pade forms, Laurent-Pade forms and two-point Pade forms.- 12.2 The T-table.- 12.3 The Pade, Laurent-Pade, and two-point Pade tables.- 13. Meromorphic functions and asymptotic behaviour.- 13.1 The function F(z).- 13.2 Asymptotics for finite Toeplitz determinants.- 13.3 Asymptotics for infinite Toeplitz determinants.- 13.4 Consequences for the T-table.- 14. Montessus de Ballore theorem for Laurent-Pade approximants.- 14.1 Semi infinite Laurent series.- 14.2 Bi-infinite Laurent series.- 15. Determination of poles.- 15.1 Rutishauser polynomials of type 1 and type 2.- 15.2 Rutishauser polynomials of type 3.- 15.3 Rutishauser polynomials and Laurent series.- 15.4 Convergence of parameters.- 16. Determination of zeros.- 16.1 Dual Rutishauser polynomials and semi-infinite series.- 16.2 From semi-infinite to bi-infinite series.- 16.3 Convergence of parameters.- 17. Convergence in a row of the Laurent-Pade table.- 17.1 Toeplitz operators and the projection method.- 17.2 Convergence of the denominator.- 17.3 Convergence of the numerator.- 18. The positive definite case and applications.- 18.1 Function classes.- 18.2 Connection with the previous results.- 18.3 Stochastic processes and systems.- 18.4 Lossless inverse scattering and transmission lines.- 18.5 Laurent-Pade approximation and ARMA-filtering.- 18.6 Concluding remarks.- 19. Examples.- 19.1 Example 1.- 19.2 Example 2.- 19.3 Example 3.- References.- List of symbols.
Series Title: Operator theory, advances and applications, v. 27.
Responsibility: Adhemar Bultheel.
More information:

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/16647917> # Laurent series and their Padé approximations
    a schema:CreativeWork, schema:Book ;
   library:oclcnum "16647917" ;
   library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/12832081#Place/basel> ; # Basel
   library:placeOfPublication <http://dbpedia.org/resource/Boston> ; # Boston
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/sz> ;
   schema:about <http://experiment.worldcat.org/entity/work/data/12832081#Topic/laurent_series> ; # Laurent series
   schema:about <http://id.worldcat.org/fast/1050307> ; # Padé approximant
   schema:about <http://experiment.worldcat.org/entity/work/data/12832081#Topic/pade_approximants_de> ; # Padé, Approximants de
   schema:about <http://experiment.worldcat.org/entity/work/data/12832081#Topic/pade_approximant> ; # Padé approximant
   schema:about <http://experiment.worldcat.org/entity/work/data/12832081#Topic/laurent_series_de> ; # Laurent, Séries de
   schema:about <http://dewey.info/class/515/e19/> ;
   schema:about <http://experiment.worldcat.org/entity/work/data/12832081#Topic/pade_naherung> ; # Padé-Näherung
   schema:about <http://experiment.worldcat.org/entity/work/data/12832081#Topic/laurent_entwicklung> ; # Laurent-Entwicklung
   schema:about <http://id.worldcat.org/fast/993644> ; # Laurent series
   schema:about <http://experiment.worldcat.org/entity/work/data/12832081#Topic/laurent_reihe> ; # Laurent-Reihe
   schema:bookFormat bgn:PrintBook ;
   schema:creator <http://viaf.org/viaf/68995789> ; # Adhemar Bultheel
   schema:datePublished "1987" ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/12832081> ;
   schema:inLanguage "en" ;
   schema:isPartOf <http://experiment.worldcat.org/entity/work/data/12832081#Series/operator_theory_advances_and_applications> ; # Operator theory, advances and applications ;
   schema:isSimilarTo <http://www.worldcat.org/oclc/623756191> ;
   schema:name "Laurent series and their Padé approximations"@en ;
   schema:productID "16647917" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/16647917#PublicationEvent/basel_boston_birkhauser_verlag_1987> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/12832081#Agent/birkhauser_verlag> ; # Birkhäuser Verlag
   schema:url <http://www.gbv.de/dms/hbz/toc/ht002997498.pdf> ;
   schema:url <http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=2152175&custom%5Fatt%5F2=simple%5Fviewer> ;
   schema:workExample <http://worldcat.org/isbn/9780817619404> ;
   schema:workExample <http://worldcat.org/isbn/9783764319403> ;
   umbel:isLike <http://d-nb.info/870976257> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/16647917> ;
    .


Related Entities

<http://dbpedia.org/resource/Boston> # Boston
    a schema:Place ;
   schema:name "Boston" ;
    .

<http://experiment.worldcat.org/entity/work/data/12832081#Agent/birkhauser_verlag> # Birkhäuser Verlag
    a bgn:Agent ;
   schema:name "Birkhäuser Verlag" ;
    .

<http://experiment.worldcat.org/entity/work/data/12832081#Series/operator_theory_advances_and_applications> # Operator theory, advances and applications ;
    a bgn:PublicationSeries ;
   schema:hasPart <http://www.worldcat.org/oclc/16647917> ; # Laurent series and their Padé approximations
   schema:name "Operator theory, advances and applications ;" ;
    .

<http://experiment.worldcat.org/entity/work/data/12832081#Topic/laurent_entwicklung> # Laurent-Entwicklung
    a schema:Intangible ;
   schema:name "Laurent-Entwicklung"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/12832081#Topic/laurent_series_de> # Laurent, Séries de
    a schema:Intangible ;
   schema:name "Laurent, Séries de"@en ;
   schema:name "Laurent, Séries de"@fr ;
    .

<http://experiment.worldcat.org/entity/work/data/12832081#Topic/pade_approximants_de> # Padé, Approximants de
    a schema:Intangible ;
   schema:name "Padé, Approximants de"@en ;
   schema:name "Padé, Approximants de"@fr ;
    .

<http://id.worldcat.org/fast/1050307> # Padé approximant
    a schema:Intangible ;
   schema:name "Padé approximant"@en ;
    .

<http://id.worldcat.org/fast/993644> # Laurent series
    a schema:Intangible ;
   schema:name "Laurent series"@en ;
    .

<http://viaf.org/viaf/68995789> # Adhemar Bultheel
    a schema:Person ;
   schema:familyName "Bultheel" ;
   schema:givenName "Adhemar" ;
   schema:name "Adhemar Bultheel" ;
    .

<http://worldcat.org/isbn/9780817619404>
    a schema:ProductModel ;
   schema:isbn "0817619402" ;
   schema:isbn "9780817619404" ;
    .

<http://worldcat.org/isbn/9783764319403>
    a schema:ProductModel ;
   schema:isbn "3764319402" ;
   schema:isbn "9783764319403" ;
    .

<http://www.worldcat.org/oclc/623756191>
    a schema:CreativeWork ;
   rdfs:label "Laurent series and their Padé approximations." ;
   schema:description "Online version:" ;
   schema:isSimilarTo <http://www.worldcat.org/oclc/16647917> ; # Laurent series and their Padé approximations
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.