Numerical Methods for Eigenvalue Problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
2012
|
| Schriftenreihe: | De Gruyter textbook
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Preface; 1 Introduction; 1.1 Example: Structural mechanics; 1.2 Example: Stochastic processes; 1.3 Example: Systems of linear differential equations; 2 Existence and properties of eigenvalues and eigenvectors; 2.1 Eigenvalues and eigenvectors; 2.2 Characteristic polynomials; 2.3 Similarity transformations; 2.4 Some properties of Hilbert spaces; 2.5 Invariant subspaces; 2.6 Schur decomposition; 2.7 Non-unitary transformations; 3 Jacobi iteration; 3.1 Iterated similarity transformations; 3.2 Two-dimensional Schur decomposition; 3.3 One step of the iteration; 3.4 Error estimates 3.5 Quadratic convergence4 Power methods; 4.1 Power iteration; 4.2 Rayleigh quotient; 4.3 Residual-based error control; 4.4 Inverse iteration; 4.5 Rayleigh iteration; 4.6 Convergence to invariant subspace; 4.7 Simultaneous iteration; 4.8 Convergence for general matrices; 5 QR iteration; 5.1 Basic QR step; 5.2 Hessenberg form; 5.3 Shifting; 5.4 Deflation; 5.5 Implicit iteration; 5.6 Multiple-shift strategies; 6 Bisection methods; 6.1 Sturm chains; 6.2 Gershgorin discs; 7 Krylov subspace methods for large sparse eigenvalue problems; 7.1 Sparse matrices and projection methods 7.2 Krylov subspaces7.3 Gram-Schmidt process; 7.4 Arnoldi iteration; 7.5 Symmetric Lanczos algorithm; 7.6 Chebyshev polynomials; 7.7 Convergence of Krylov subspace methods; 8 Generalized and polynomial eigenvalue problems; 8.1 Polynomial eigenvalue problems and linearization; 8.2 Matrix pencils; 8.3 Deflating subspaces and the generalized Schur decomposition; 8.4 Hessenberg-triangular form; 8.5 Deflation; 8.6 The QZ step; Bibliography; Index This textbook presents a number of the most important numerical methods for finding eigenvalues and eigenvectors of matrices. The authors discuss the central ideas underlying the different algorithms and introduce the theoretical concepts required to analyze their behaviour. Several programming examples allow the reader to experience the behaviour of the different algorithms first-hand. The book addresses students and lecturers of mathematics and engineering who are interested in the fundamental ideas of modern numerical methods and want to learn how to apply and extend these ideas to solve ne |
| Beschreibung: | 1 Online-Ressource (216 pages) |
| ISBN: | 9783110250374 3110250373 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV043166531 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 151126s2012 |||| o||u| ||||||eng d | ||
| 020 | |a 9783110250374 |c electronic bk. |9 978-3-11-025037-4 | ||
| 020 | |a 3110250373 |c electronic bk. |9 3-11-025037-3 | ||
| 035 | |a (OCoLC)796384303 | ||
| 035 | |a (DE-599)BVBBV043166531 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 082 | 0 | |a 512.9/436 | |
| 082 | 0 | |a 512.9436 | |
| 100 | 1 | |a Börm, Steffen |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Numerical Methods for Eigenvalue Problems |
| 264 | 1 | |a Berlin |b De Gruyter |c 2012 | |
| 300 | |a 1 Online-Ressource (216 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter textbook | |
| 500 | |a Preface; 1 Introduction; 1.1 Example: Structural mechanics; 1.2 Example: Stochastic processes; 1.3 Example: Systems of linear differential equations; 2 Existence and properties of eigenvalues and eigenvectors; 2.1 Eigenvalues and eigenvectors; 2.2 Characteristic polynomials; 2.3 Similarity transformations; 2.4 Some properties of Hilbert spaces; 2.5 Invariant subspaces; 2.6 Schur decomposition; 2.7 Non-unitary transformations; 3 Jacobi iteration; 3.1 Iterated similarity transformations; 3.2 Two-dimensional Schur decomposition; 3.3 One step of the iteration; 3.4 Error estimates | ||
| 500 | |a 3.5 Quadratic convergence4 Power methods; 4.1 Power iteration; 4.2 Rayleigh quotient; 4.3 Residual-based error control; 4.4 Inverse iteration; 4.5 Rayleigh iteration; 4.6 Convergence to invariant subspace; 4.7 Simultaneous iteration; 4.8 Convergence for general matrices; 5 QR iteration; 5.1 Basic QR step; 5.2 Hessenberg form; 5.3 Shifting; 5.4 Deflation; 5.5 Implicit iteration; 5.6 Multiple-shift strategies; 6 Bisection methods; 6.1 Sturm chains; 6.2 Gershgorin discs; 7 Krylov subspace methods for large sparse eigenvalue problems; 7.1 Sparse matrices and projection methods | ||
| 500 | |a 7.2 Krylov subspaces7.3 Gram-Schmidt process; 7.4 Arnoldi iteration; 7.5 Symmetric Lanczos algorithm; 7.6 Chebyshev polynomials; 7.7 Convergence of Krylov subspace methods; 8 Generalized and polynomial eigenvalue problems; 8.1 Polynomial eigenvalue problems and linearization; 8.2 Matrix pencils; 8.3 Deflating subspaces and the generalized Schur decomposition; 8.4 Hessenberg-triangular form; 8.5 Deflation; 8.6 The QZ step; Bibliography; Index | ||
| 500 | |a This textbook presents a number of the most important numerical methods for finding eigenvalues and eigenvectors of matrices. The authors discuss the central ideas underlying the different algorithms and introduce the theoretical concepts required to analyze their behaviour. Several programming examples allow the reader to experience the behaviour of the different algorithms first-hand. The book addresses students and lecturers of mathematics and engineering who are interested in the fundamental ideas of modern numerical methods and want to learn how to apply and extend these ideas to solve ne | ||
| 650 | 4 | |a Matrices / Data processing | |
| 650 | 7 | |a MATHEMATICS / Algebra / Elementary |2 bisacsh | |
| 650 | 7 | |a Eigenvalues |2 fast | |
| 650 | 7 | |a Eigenvectors |2 fast | |
| 650 | 7 | |a Matrices / Data processing |2 fast | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Eigenvalues | |
| 650 | 4 | |a Eigenvectors | |
| 650 | 4 | |a Matrices |x Data processing | |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Eigenwertproblem |0 (DE-588)4013802-1 |2 gnd |9 rswk-swf |
| 655 | 7 | |8 1\p |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Eigenwertproblem |0 (DE-588)4013802-1 |D s |
| 689 | 0 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | |8 2\p |5 DE-604 | |
| 700 | 1 | |a Mehl, Christian |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=471055 |x Aggregator |3 Volltext |
| 912 | |a ZDB-4-EBA | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-028590722 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804175642203258880 |
|---|---|
| any_adam_object | |
| author | Börm, Steffen |
| author_facet | Börm, Steffen |
| author_role | aut |
| author_sort | Börm, Steffen |
| author_variant | s b sb |
| building | Verbundindex |
| bvnumber | BV043166531 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)796384303 (DE-599)BVBBV043166531 |
| dewey-full | 512.9/436 512.9436 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/436 512.9436 |
| dewey-search | 512.9/436 512.9436 |
| dewey-sort | 3512.9 3436 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04196nmm a2200577zc 4500</leader><controlfield tag="001">BV043166531</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">151126s2012 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110250374</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">978-3-11-025037-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3110250373</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">3-11-025037-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)796384303</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043166531</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.9/436</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.9436</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Börm, Steffen</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Numerical Methods for Eigenvalue Problems</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin</subfield><subfield code="b">De Gruyter</subfield><subfield code="c">2012</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (216 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">De Gruyter textbook</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Preface; 1 Introduction; 1.1 Example: Structural mechanics; 1.2 Example: Stochastic processes; 1.3 Example: Systems of linear differential equations; 2 Existence and properties of eigenvalues and eigenvectors; 2.1 Eigenvalues and eigenvectors; 2.2 Characteristic polynomials; 2.3 Similarity transformations; 2.4 Some properties of Hilbert spaces; 2.5 Invariant subspaces; 2.6 Schur decomposition; 2.7 Non-unitary transformations; 3 Jacobi iteration; 3.1 Iterated similarity transformations; 3.2 Two-dimensional Schur decomposition; 3.3 One step of the iteration; 3.4 Error estimates</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">3.5 Quadratic convergence4 Power methods; 4.1 Power iteration; 4.2 Rayleigh quotient; 4.3 Residual-based error control; 4.4 Inverse iteration; 4.5 Rayleigh iteration; 4.6 Convergence to invariant subspace; 4.7 Simultaneous iteration; 4.8 Convergence for general matrices; 5 QR iteration; 5.1 Basic QR step; 5.2 Hessenberg form; 5.3 Shifting; 5.4 Deflation; 5.5 Implicit iteration; 5.6 Multiple-shift strategies; 6 Bisection methods; 6.1 Sturm chains; 6.2 Gershgorin discs; 7 Krylov subspace methods for large sparse eigenvalue problems; 7.1 Sparse matrices and projection methods</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">7.2 Krylov subspaces7.3 Gram-Schmidt process; 7.4 Arnoldi iteration; 7.5 Symmetric Lanczos algorithm; 7.6 Chebyshev polynomials; 7.7 Convergence of Krylov subspace methods; 8 Generalized and polynomial eigenvalue problems; 8.1 Polynomial eigenvalue problems and linearization; 8.2 Matrix pencils; 8.3 Deflating subspaces and the generalized Schur decomposition; 8.4 Hessenberg-triangular form; 8.5 Deflation; 8.6 The QZ step; Bibliography; Index</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This textbook presents a number of the most important numerical methods for finding eigenvalues and eigenvectors of matrices. The authors discuss the central ideas underlying the different algorithms and introduce the theoretical concepts required to analyze their behaviour. Several programming examples allow the reader to experience the behaviour of the different algorithms first-hand. The book addresses students and lecturers of mathematics and engineering who are interested in the fundamental ideas of modern numerical methods and want to learn how to apply and extend these ideas to solve ne</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Matrices / Data processing</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Algebra / Elementary</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Eigenvalues</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Eigenvectors</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Matrices / Data processing</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Datenverarbeitung</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Eigenvalues</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Eigenvectors</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Matrices</subfield><subfield code="x">Data processing</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Numerisches Verfahren</subfield><subfield code="0">(DE-588)4128130-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Eigenwertproblem</subfield><subfield code="0">(DE-588)4013802-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="8">1\p</subfield><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Eigenwertproblem</subfield><subfield code="0">(DE-588)4013802-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Numerisches Verfahren</subfield><subfield code="0">(DE-588)4128130-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Mehl, Christian</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=471055</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-028590722</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="883" ind1="1" ind2=" "><subfield code="8">2\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></record></collection> |
| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV043166531 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:19:32Z |
| institution | BVB |
| isbn | 9783110250374 3110250373 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028590722 |
| oclc_num | 796384303 |
| open_access_boolean | |
| physical | 1 Online-Ressource (216 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter textbook |
| spelling | Börm, Steffen Verfasser aut Numerical Methods for Eigenvalue Problems Berlin De Gruyter 2012 1 Online-Ressource (216 pages) txt rdacontent c rdamedia cr rdacarrier De Gruyter textbook Preface; 1 Introduction; 1.1 Example: Structural mechanics; 1.2 Example: Stochastic processes; 1.3 Example: Systems of linear differential equations; 2 Existence and properties of eigenvalues and eigenvectors; 2.1 Eigenvalues and eigenvectors; 2.2 Characteristic polynomials; 2.3 Similarity transformations; 2.4 Some properties of Hilbert spaces; 2.5 Invariant subspaces; 2.6 Schur decomposition; 2.7 Non-unitary transformations; 3 Jacobi iteration; 3.1 Iterated similarity transformations; 3.2 Two-dimensional Schur decomposition; 3.3 One step of the iteration; 3.4 Error estimates 3.5 Quadratic convergence4 Power methods; 4.1 Power iteration; 4.2 Rayleigh quotient; 4.3 Residual-based error control; 4.4 Inverse iteration; 4.5 Rayleigh iteration; 4.6 Convergence to invariant subspace; 4.7 Simultaneous iteration; 4.8 Convergence for general matrices; 5 QR iteration; 5.1 Basic QR step; 5.2 Hessenberg form; 5.3 Shifting; 5.4 Deflation; 5.5 Implicit iteration; 5.6 Multiple-shift strategies; 6 Bisection methods; 6.1 Sturm chains; 6.2 Gershgorin discs; 7 Krylov subspace methods for large sparse eigenvalue problems; 7.1 Sparse matrices and projection methods 7.2 Krylov subspaces7.3 Gram-Schmidt process; 7.4 Arnoldi iteration; 7.5 Symmetric Lanczos algorithm; 7.6 Chebyshev polynomials; 7.7 Convergence of Krylov subspace methods; 8 Generalized and polynomial eigenvalue problems; 8.1 Polynomial eigenvalue problems and linearization; 8.2 Matrix pencils; 8.3 Deflating subspaces and the generalized Schur decomposition; 8.4 Hessenberg-triangular form; 8.5 Deflation; 8.6 The QZ step; Bibliography; Index This textbook presents a number of the most important numerical methods for finding eigenvalues and eigenvectors of matrices. The authors discuss the central ideas underlying the different algorithms and introduce the theoretical concepts required to analyze their behaviour. Several programming examples allow the reader to experience the behaviour of the different algorithms first-hand. The book addresses students and lecturers of mathematics and engineering who are interested in the fundamental ideas of modern numerical methods and want to learn how to apply and extend these ideas to solve ne Matrices / Data processing MATHEMATICS / Algebra / Elementary bisacsh Eigenvalues fast Eigenvectors fast Matrices / Data processing fast Datenverarbeitung Eigenvalues Eigenvectors Matrices Data processing Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Eigenwertproblem (DE-588)4013802-1 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Eigenwertproblem (DE-588)4013802-1 s Numerisches Verfahren (DE-588)4128130-5 s 2\p DE-604 Mehl, Christian Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=471055 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Börm, Steffen Numerical Methods for Eigenvalue Problems Matrices / Data processing MATHEMATICS / Algebra / Elementary bisacsh Eigenvalues fast Eigenvectors fast Matrices / Data processing fast Datenverarbeitung Eigenvalues Eigenvectors Matrices Data processing Numerisches Verfahren (DE-588)4128130-5 gnd Eigenwertproblem (DE-588)4013802-1 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4013802-1 (DE-588)4123623-3 |
| title | Numerical Methods for Eigenvalue Problems |
| title_auth | Numerical Methods for Eigenvalue Problems |
| title_exact_search | Numerical Methods for Eigenvalue Problems |
| title_full | Numerical Methods for Eigenvalue Problems |
| title_fullStr | Numerical Methods for Eigenvalue Problems |
| title_full_unstemmed | Numerical Methods for Eigenvalue Problems |
| title_short | Numerical Methods for Eigenvalue Problems |
| title_sort | numerical methods for eigenvalue problems |
| topic | Matrices / Data processing MATHEMATICS / Algebra / Elementary bisacsh Eigenvalues fast Eigenvectors fast Matrices / Data processing fast Datenverarbeitung Eigenvalues Eigenvectors Matrices Data processing Numerisches Verfahren (DE-588)4128130-5 gnd Eigenwertproblem (DE-588)4013802-1 gnd |
| topic_facet | Matrices / Data processing MATHEMATICS / Algebra / Elementary Eigenvalues Eigenvectors Datenverarbeitung Matrices Data processing Numerisches Verfahren Eigenwertproblem Lehrbuch |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=471055 |
| work_keys_str_mv | AT bormsteffen numericalmethodsforeigenvalueproblems AT mehlchristian numericalmethodsforeigenvalueproblems |