Guaranteed Accuracy in Numerical Linear Algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1993
|
| Schriftenreihe: | Mathematics and Its Applications
252 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | There exists a vast literature on numerical methods of linear algebra. In our bibliography list, which is by far not complete, we included some monographs on the subject [46], [15], [32], [39], [11], [21]. The present book is devoted to the theory of algorithms for a single problem of linear algebra, namely, for the problem of solving systems of linear equations with non-full-rank matrix of coefficients. The solution of this problem splits into many steps, the detailed discussion of which are interest ing problems on their own (bidiagonalization of matrices, computation of singular values and eigenvalues, procedures of deflation of singular values, etc. ). Moreover, the theory of algorithms for solutions of the symmetric eigenvalues problem is closely related to the theory of solv ing linear systems (Householder's algorithms of bidiagonalization and tridiagonalization, eigenvalues and singular values, etc. ). It should be stressed that in this book we discuss algorithms which to computer programs having the virtue that the accuracy of com lead putations is guaranteed. As far as the final program product is con cerned, this means that the user always finds an unambiguous solution of his problem. This solution might be of two kinds: 1. Solution of the problem with an estimate of errors, where abso lutely all errors of input data and machine round-offs are taken into account. 2 |
| Beschreibung: | 1 Online-Ressource (XI, 537 p) |
| ISBN: | 9789401119528 9789401048637 |
| DOI: | 10.1007/978-94-011-1952-8 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042423869 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1993 |||| o||u| ||||||eng d | ||
| 020 | |a 9789401119528 |c Online |9 978-94-011-1952-8 | ||
| 020 | |a 9789401048637 |c Print |9 978-94-010-4863-7 | ||
| 024 | 7 | |a 10.1007/978-94-011-1952-8 |2 doi | |
| 035 | |a (OCoLC)1184488720 | ||
| 035 | |a (DE-599)BVBBV042423869 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 518 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Godunov, S. K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Guaranteed Accuracy in Numerical Linear Algebra |c by S. K. Godunov, A. G. Antonov, O. P. Kiriljuk, V. I. Kostin |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 1993 | |
| 300 | |a 1 Online-Ressource (XI, 537 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Mathematics and Its Applications |v 252 | |
| 500 | |a There exists a vast literature on numerical methods of linear algebra. In our bibliography list, which is by far not complete, we included some monographs on the subject [46], [15], [32], [39], [11], [21]. The present book is devoted to the theory of algorithms for a single problem of linear algebra, namely, for the problem of solving systems of linear equations with non-full-rank matrix of coefficients. The solution of this problem splits into many steps, the detailed discussion of which are interest ing problems on their own (bidiagonalization of matrices, computation of singular values and eigenvalues, procedures of deflation of singular values, etc. ). Moreover, the theory of algorithms for solutions of the symmetric eigenvalues problem is closely related to the theory of solv ing linear systems (Householder's algorithms of bidiagonalization and tridiagonalization, eigenvalues and singular values, etc. ). It should be stressed that in this book we discuss algorithms which to computer programs having the virtue that the accuracy of com lead putations is guaranteed. As far as the final program product is con cerned, this means that the user always finds an unambiguous solution of his problem. This solution might be of two kinds: 1. Solution of the problem with an estimate of errors, where abso lutely all errors of input data and machine round-offs are taken into account. 2 | ||
| 650 | 4 | |a Computer science | |
| 650 | 4 | |a Electronic data processing | |
| 650 | 4 | |a Matrix theory | |
| 650 | 4 | |a Computer Science | |
| 650 | 4 | |a Numeric Computing | |
| 650 | 4 | |a Linear and Multilinear Algebras, Matrix Theory | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Informatik | |
| 650 | 0 | 7 | |a Numerische Mathematik |0 (DE-588)4042805-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algorithmus |0 (DE-588)4001183-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineare Algebra |0 (DE-588)4035811-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Algebra |0 (DE-588)4035811-2 |D s |
| 689 | 0 | 1 | |a Algorithmus |0 (DE-588)4001183-5 |D s |
| 689 | 0 | 2 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Numerische Mathematik |0 (DE-588)4042805-9 |D s |
| 689 | 1 | 1 | |a Lineare Algebra |0 (DE-588)4035811-2 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 700 | 1 | |a Antonov, A. G. |e Sonstige |4 oth | |
| 700 | 1 | |a Kiriljuk, O. P. |e Sonstige |4 oth | |
| 700 | 1 | |a Kostin, V. I. |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-94-011-1952-8 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027859286 | ||
| 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_ | 1804153100135563264 |
|---|---|
| any_adam_object | |
| author | Godunov, S. K. |
| author_facet | Godunov, S. K. |
| author_role | aut |
| author_sort | Godunov, S. K. |
| author_variant | s k g sk skg |
| building | Verbundindex |
| bvnumber | BV042423869 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184488720 (DE-599)BVBBV042423869 |
| dewey-full | 518 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518 |
| dewey-search | 518 |
| dewey-sort | 3518 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-011-1952-8 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03822nmm a2200649zcb4500</leader><controlfield tag="001">BV042423869</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1993 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401119528</subfield><subfield code="c">Online</subfield><subfield code="9">978-94-011-1952-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401048637</subfield><subfield code="c">Print</subfield><subfield code="9">978-94-010-4863-7</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-94-011-1952-8</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1184488720</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042423869</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="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">518</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Godunov, S. K.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Guaranteed Accuracy in Numerical Linear Algebra</subfield><subfield code="c">by S. K. Godunov, A. G. Antonov, O. P. Kiriljuk, V. I. Kostin</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht</subfield><subfield code="b">Springer Netherlands</subfield><subfield code="c">1993</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XI, 537 p)</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">Mathematics and Its Applications</subfield><subfield code="v">252</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">There exists a vast literature on numerical methods of linear algebra. In our bibliography list, which is by far not complete, we included some monographs on the subject [46], [15], [32], [39], [11], [21]. The present book is devoted to the theory of algorithms for a single problem of linear algebra, namely, for the problem of solving systems of linear equations with non-full-rank matrix of coefficients. The solution of this problem splits into many steps, the detailed discussion of which are interest ing problems on their own (bidiagonalization of matrices, computation of singular values and eigenvalues, procedures of deflation of singular values, etc. ). Moreover, the theory of algorithms for solutions of the symmetric eigenvalues problem is closely related to the theory of solv ing linear systems (Householder's algorithms of bidiagonalization and tridiagonalization, eigenvalues and singular values, etc. ). It should be stressed that in this book we discuss algorithms which to computer programs having the virtue that the accuracy of com lead putations is guaranteed. As far as the final program product is con cerned, this means that the user always finds an unambiguous solution of his problem. This solution might be of two kinds: 1. Solution of the problem with an estimate of errors, where abso lutely all errors of input data and machine round-offs are taken into account. 2</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer science</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Electronic data processing</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Matrix theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer Science</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Numeric Computing</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Linear and Multilinear Algebras, Matrix Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Datenverarbeitung</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Informatik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Numerische Mathematik</subfield><subfield code="0">(DE-588)4042805-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algorithmus</subfield><subfield code="0">(DE-588)4001183-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</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">Lineare Algebra</subfield><subfield code="0">(DE-588)4035811-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Lineare Algebra</subfield><subfield code="0">(DE-588)4035811-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Algorithmus</subfield><subfield code="0">(DE-588)4001183-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><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">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Numerische Mathematik</subfield><subfield code="0">(DE-588)4042805-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Lineare Algebra</subfield><subfield code="0">(DE-588)4035811-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Antonov, A. G.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kiriljuk, O. P.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kostin, V. I.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-94-011-1952-8</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027859286</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> |
| id | DE-604.BV042423869 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401119528 9789401048637 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859286 |
| oclc_num | 1184488720 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XI, 537 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer Netherlands |
| record_format | marc |
| series2 | Mathematics and Its Applications |
| spelling | Godunov, S. K. Verfasser aut Guaranteed Accuracy in Numerical Linear Algebra by S. K. Godunov, A. G. Antonov, O. P. Kiriljuk, V. I. Kostin Dordrecht Springer Netherlands 1993 1 Online-Ressource (XI, 537 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 252 There exists a vast literature on numerical methods of linear algebra. In our bibliography list, which is by far not complete, we included some monographs on the subject [46], [15], [32], [39], [11], [21]. The present book is devoted to the theory of algorithms for a single problem of linear algebra, namely, for the problem of solving systems of linear equations with non-full-rank matrix of coefficients. The solution of this problem splits into many steps, the detailed discussion of which are interest ing problems on their own (bidiagonalization of matrices, computation of singular values and eigenvalues, procedures of deflation of singular values, etc. ). Moreover, the theory of algorithms for solutions of the symmetric eigenvalues problem is closely related to the theory of solv ing linear systems (Householder's algorithms of bidiagonalization and tridiagonalization, eigenvalues and singular values, etc. ). It should be stressed that in this book we discuss algorithms which to computer programs having the virtue that the accuracy of com lead putations is guaranteed. As far as the final program product is con cerned, this means that the user always finds an unambiguous solution of his problem. This solution might be of two kinds: 1. Solution of the problem with an estimate of errors, where abso lutely all errors of input data and machine round-offs are taken into account. 2 Computer science Electronic data processing Matrix theory Computer Science Numeric Computing Linear and Multilinear Algebras, Matrix Theory Datenverarbeitung Informatik Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s Algorithmus (DE-588)4001183-5 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Numerische Mathematik (DE-588)4042805-9 s 2\p DE-604 Antonov, A. G. Sonstige oth Kiriljuk, O. P. Sonstige oth Kostin, V. I. Sonstige oth https://doi.org/10.1007/978-94-011-1952-8 Verlag 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 | Godunov, S. K. Guaranteed Accuracy in Numerical Linear Algebra Computer science Electronic data processing Matrix theory Computer Science Numeric Computing Linear and Multilinear Algebras, Matrix Theory Datenverarbeitung Informatik Numerische Mathematik (DE-588)4042805-9 gnd Algorithmus (DE-588)4001183-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4001183-5 (DE-588)4128130-5 (DE-588)4035811-2 |
| title | Guaranteed Accuracy in Numerical Linear Algebra |
| title_auth | Guaranteed Accuracy in Numerical Linear Algebra |
| title_exact_search | Guaranteed Accuracy in Numerical Linear Algebra |
| title_full | Guaranteed Accuracy in Numerical Linear Algebra by S. K. Godunov, A. G. Antonov, O. P. Kiriljuk, V. I. Kostin |
| title_fullStr | Guaranteed Accuracy in Numerical Linear Algebra by S. K. Godunov, A. G. Antonov, O. P. Kiriljuk, V. I. Kostin |
| title_full_unstemmed | Guaranteed Accuracy in Numerical Linear Algebra by S. K. Godunov, A. G. Antonov, O. P. Kiriljuk, V. I. Kostin |
| title_short | Guaranteed Accuracy in Numerical Linear Algebra |
| title_sort | guaranteed accuracy in numerical linear algebra |
| topic | Computer science Electronic data processing Matrix theory Computer Science Numeric Computing Linear and Multilinear Algebras, Matrix Theory Datenverarbeitung Informatik Numerische Mathematik (DE-588)4042805-9 gnd Algorithmus (DE-588)4001183-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Computer science Electronic data processing Matrix theory Computer Science Numeric Computing Linear and Multilinear Algebras, Matrix Theory Datenverarbeitung Informatik Numerische Mathematik Algorithmus Numerisches Verfahren Lineare Algebra |
| url | https://doi.org/10.1007/978-94-011-1952-8 |
| work_keys_str_mv | AT godunovsk guaranteedaccuracyinnumericallinearalgebra AT antonovag guaranteedaccuracyinnumericallinearalgebra AT kiriljukop guaranteedaccuracyinnumericallinearalgebra AT kostinvi guaranteedaccuracyinnumericallinearalgebra |