Interval Analysis : : and Automatic Result Verification / / Günter Mayer.
This self-contained text is a step-by-step introduction and a complete overview of interval computation and result verification, a subject whose importance has steadily increased over the past many years. The author, an expert in the field, gently presents the theory of interval analysis through man...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2017] ©2017 |
Year of Publication: | 2017 |
Language: | English |
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Mayer, Günter, author. aut http://id.loc.gov/vocabulary/relators/aut Interval Analysis : and Automatic Result Verification / Günter Mayer. Berlin ; Boston : De Gruyter, [2017] ©2017 1 online resource (XIV, 518 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Studies in Mathematics , 0179-0986 ; 65 Frontmatter -- Preface -- Contents -- 1. Preliminaries -- 2. Real intervals -- 3. Interval vectors, interval matrices -- 4. Expressions, P-contraction, ε-inflation -- 5. Linear systems of equations -- 6. Nonlinear systems of equations -- 7. Eigenvalue problems and related ones -- 8. Automatic differentiation -- 9. Complex intervals -- Final Remarks -- Appendix -- A. Proof of the Jordan normal form -- B. Two elementary proofs of Brouwer’s fixed point theorem -- C. Proof of the Newton–Kantorovich Theorem -- D. Convergence proof of the row cyclic Jacobi method -- E. The CORDIC algorithm -- F. The symmetric solution set – a proof of Theorem 5.2.6 -- G. A short introduction to INTLAB -- Bibliography -- Symbol Index -- Author Index -- Subject Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star This self-contained text is a step-by-step introduction and a complete overview of interval computation and result verification, a subject whose importance has steadily increased over the past many years. The author, an expert in the field, gently presents the theory of interval analysis through many examples and exercises, and guides the reader from the basics of the theory to current research topics in the mathematics of computation. Contents Preliminaries Real intervals Interval vectors, interval matrices Expressions, P-contraction, ε-inflation Linear systems of equations Nonlinear systems of equations Eigenvalue problems Automatic differentiation Complex intervals Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Interval analysis (Mathematics). Automatische Differentiation. Computerarithmetik. Intervalalgebra. Intervalanalyse. Richrigkeit von Ergebnissen. MATHEMATICS / Numerical Analysis. bisacsh Title is part of eBook package: De Gruyter DG Plus DeG Package 2017 Part 1 9783110762495 Title is part of eBook package: De Gruyter DG Plus eBook-Package 2017 9783110719543 Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package 9783110494938 ZDB-23-GSM Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2017 9783110540550 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE ENGLISH 2017 9783110625264 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2017 9783110548204 ZDB-23-DMA EPUB 9783110498059 print 9783110500639 https://doi.org/10.1515/9783110499469 https://www.degruyter.com/isbn/9783110499469 Cover https://www.degruyter.com/document/cover/isbn/9783110499469/original |
language |
English |
format |
eBook |
author |
Mayer, Günter, Mayer, Günter, |
spellingShingle |
Mayer, Günter, Mayer, Günter, Interval Analysis : and Automatic Result Verification / De Gruyter Studies in Mathematics , Frontmatter -- Preface -- Contents -- 1. Preliminaries -- 2. Real intervals -- 3. Interval vectors, interval matrices -- 4. Expressions, P-contraction, ε-inflation -- 5. Linear systems of equations -- 6. Nonlinear systems of equations -- 7. Eigenvalue problems and related ones -- 8. Automatic differentiation -- 9. Complex intervals -- Final Remarks -- Appendix -- A. Proof of the Jordan normal form -- B. Two elementary proofs of Brouwer’s fixed point theorem -- C. Proof of the Newton–Kantorovich Theorem -- D. Convergence proof of the row cyclic Jacobi method -- E. The CORDIC algorithm -- F. The symmetric solution set – a proof of Theorem 5.2.6 -- G. A short introduction to INTLAB -- Bibliography -- Symbol Index -- Author Index -- Subject Index |
author_facet |
Mayer, Günter, Mayer, Günter, |
author_variant |
g m gm g m gm |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Mayer, Günter, |
title |
Interval Analysis : and Automatic Result Verification / |
title_sub |
and Automatic Result Verification / |
title_full |
Interval Analysis : and Automatic Result Verification / Günter Mayer. |
title_fullStr |
Interval Analysis : and Automatic Result Verification / Günter Mayer. |
title_full_unstemmed |
Interval Analysis : and Automatic Result Verification / Günter Mayer. |
title_auth |
Interval Analysis : and Automatic Result Verification / |
title_alt |
Frontmatter -- Preface -- Contents -- 1. Preliminaries -- 2. Real intervals -- 3. Interval vectors, interval matrices -- 4. Expressions, P-contraction, ε-inflation -- 5. Linear systems of equations -- 6. Nonlinear systems of equations -- 7. Eigenvalue problems and related ones -- 8. Automatic differentiation -- 9. Complex intervals -- Final Remarks -- Appendix -- A. Proof of the Jordan normal form -- B. Two elementary proofs of Brouwer’s fixed point theorem -- C. Proof of the Newton–Kantorovich Theorem -- D. Convergence proof of the row cyclic Jacobi method -- E. The CORDIC algorithm -- F. The symmetric solution set – a proof of Theorem 5.2.6 -- G. A short introduction to INTLAB -- Bibliography -- Symbol Index -- Author Index -- Subject Index |
title_new |
Interval Analysis : |
title_sort |
interval analysis : and automatic result verification / |
series |
De Gruyter Studies in Mathematics , |
series2 |
De Gruyter Studies in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2017 |
physical |
1 online resource (XIV, 518 p.) Issued also in print. |
contents |
Frontmatter -- Preface -- Contents -- 1. Preliminaries -- 2. Real intervals -- 3. Interval vectors, interval matrices -- 4. Expressions, P-contraction, ε-inflation -- 5. Linear systems of equations -- 6. Nonlinear systems of equations -- 7. Eigenvalue problems and related ones -- 8. Automatic differentiation -- 9. Complex intervals -- Final Remarks -- Appendix -- A. Proof of the Jordan normal form -- B. Two elementary proofs of Brouwer’s fixed point theorem -- C. Proof of the Newton–Kantorovich Theorem -- D. Convergence proof of the row cyclic Jacobi method -- E. The CORDIC algorithm -- F. The symmetric solution set – a proof of Theorem 5.2.6 -- G. A short introduction to INTLAB -- Bibliography -- Symbol Index -- Author Index -- Subject Index |
isbn |
9783110499469 9783110762495 9783110719543 9783110494938 9783110540550 9783110625264 9783110548204 9783110498059 9783110500639 |
issn |
0179-0986 ; |
url |
https://doi.org/10.1515/9783110499469 https://www.degruyter.com/isbn/9783110499469 https://www.degruyter.com/document/cover/isbn/9783110499469/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
519 - Probabilities & applied mathematics |
dewey-full |
519.4 |
dewey-sort |
3519.4 |
dewey-raw |
519.4 |
dewey-search |
519.4 |
doi_str_mv |
10.1515/9783110499469 |
oclc_num |
984647843 |
work_keys_str_mv |
AT mayergunter intervalanalysisandautomaticresultverification |
status_str |
n |
ids_txt_mv |
(DE-B1597)470629 (OCoLC)984647843 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2017 Part 1 Title is part of eBook package: De Gruyter DG Plus eBook-Package 2017 Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2017 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE ENGLISH 2017 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2017 |
is_hierarchy_title |
Interval Analysis : and Automatic Result Verification / |
container_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2017 Part 1 |
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1770177654439280640 |
fullrecord |
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