Interval analysis : and automatic result verification
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...
Saved in:
| Main Author | |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
Berlin
De Gruyter
2017
Walter de Gruyter GmbH |
| Edition | 1 |
| Series | De Gruyter Studies in Mathematics |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9783110500639 3110500639 3110498057 9783110498059 |
| DOI | 10.1515/9783110499469 |
Cover
Loading…
| Abstract | 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, ? -inflation * Linear systems of equations * Nonlinear systems of equations * Eigenvalue problems * Automatic differentiation * Complex intervals * |
|---|---|
| AbstractList | 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 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, e-inflation Linear systems of equations Nonlinear systems of equations Eigenvalue problems Automatic differentiation Complex intervals 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, ? -inflation * Linear systems of equations * Nonlinear systems of equations * Eigenvalue problems * Automatic differentiation * Complex intervals * The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. 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. |
| Author | Mayer, Günter |
| Author_xml | – sequence: 1 fullname: Mayer, Günter |
| BackLink | https://cir.nii.ac.jp/crid/1130282269716705920$$DView record in CiNii |
| BookMark | eNqNjztPwzAUhY14iFI6MrFkQEIMBT_iFxtUBSpVYkGskePclFA3gThp1X-PaSpExcJi3-Pz6VyfE3RQViUgdEbwNeGE32ipGCE41joWeg8NdvT-j-YYC6aPUE8rJhljUh6jgffvGGOigqS8h_ikbKBeGheZ0ri1L3x0G8YsMm1TLUxT2KgG37omWkJd5IUNT1V5ig5z4zwMtncfvT6MX0ZPw-nz42R0Nx0apgmTwzSOwcg8B2yDxljlWU5jLRQHBdqaXMUKZMYwpymmGRMiTQVYRbLU2IxnrI-uumDj57Dyb5VrfLJ0kFbV3Cc7vf_LKsx_sSvjQv8MZnW7DkOyMLX9k3vZsR919dmCb5JNpIWyqY1LxvejWMWMMhHI8y0JtYNZlXSrBQndaXAvOrcsisQW3-fGUJQKLYmQ4WMUsy8yY4rB |
| ContentType | eBook Book |
| DBID | RYH YSPEL |
| DEWEY | 519.4 |
| DOI | 10.1515/9783110499469 |
| DatabaseName | CiNii Complete Perlego |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics |
| EISBN | 9783110499469 3110499460 3110498057 9783110498059 |
| Edition | 1 1st edition. |
| ExternalDocumentID | 9783110499469 9783110498059 EBC4843236 611302 BB2352522X |
| Genre | Electronic books |
| GroupedDBID | -VX 20A 38. AABBV AAHDW AAUSU AAZEP ABARN ABHWV ABMRC ABONK ABQPQ ABYVA ACBYE ACEOT ACISH ACLGV ADDXO ADOUC ADPYN ADVEM ADVQQ ADZGP AEAED AEDVL AEQJM AERYV AETUO AEYCP AFHFQ AFOJC AFRFP AGLJD AHWGJ AIOLA AIUUY AIXPE AJFER ALMA_UNASSIGNED_HOLDINGS ARPAB ARSQP AZZ BBABE BFRBX BHFIF CZZ DLQEV DUGUG EBSCA ECOWB GEOUK MYL OHILO PQQKQ QD8 RYH XI1 YSPEL AVGCG ABCRS AGIZT AMYDA I4C |
| ID | FETCH-LOGICAL-a39137-b44ea7ffe0c913008fdf249685e8e9caf848e7d3052b02d366bb6ec81dbacd5d3 |
| ISBN | 9783110500639 3110500639 3110498057 9783110498059 |
| IngestDate | Fri Nov 08 05:34:10 EST 2024 Fri Nov 08 05:15:17 EST 2024 Thu Aug 14 17:50:49 EDT 2025 Wed Sep 03 01:06:41 EDT 2025 Tue Sep 02 23:07:39 EDT 2025 Thu Jun 26 23:24:44 EDT 2025 |
| IsPeerReviewed | false |
| IsScholarly | false |
| LCCallNum_Ident | QA297.75.M394 2017eb |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-a39137-b44ea7ffe0c913008fdf249685e8e9caf848e7d3052b02d366bb6ec81dbacd5d3 |
| Notes | Includes bibliographical references (p. [483]-498) and indexes |
| OCLC | 983733377 984647843 |
| PQID | EBC4843236 |
| PageCount | 1 online resource (532 pages) |
| ParticipantIDs | askewsholts_vlebooks_9783110499469 askewsholts_vlebooks_9783110498059 walterdegruyter_marc_9783110499469 proquest_ebookcentral_EBC4843236 perlego_books_611302 nii_cinii_1130282269716705920 |
| PublicationCentury | 2000 |
| PublicationDate | c2017 2017 [2017] 2017-04-10 |
| PublicationDateYYYYMMDD | 2017-01-01 2017-04-10 |
| PublicationDate_xml | – year: 2017 text: 2017 |
| PublicationDecade | 2010 |
| PublicationPlace | Berlin |
| PublicationPlace_xml | – name: Berlin – name: Berlin/Boston – name: Boston |
| PublicationSeriesTitle | De Gruyter Studies in Mathematics |
| PublicationYear | 2017 |
| Publisher | De Gruyter Walter de Gruyter GmbH |
| Publisher_xml | – name: De Gruyter – name: Walter de Gruyter GmbH |
| RestrictionsOnAccess | restricted access |
| SSID | ssj0001833725 ssj0003401084 ssib046649694 ssib036171366 |
| Score | 2.0999153 |
| Snippet | 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... The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from... |
| SourceID | askewsholts walterdegruyter proquest perlego nii |
| SourceType | Aggregation Database Publisher |
| SubjectTerms | Automatische Differentiation Computerarithmetik Interval analysis (Mathematics) Intervalalgebra Intervalanalyse MATHEMATICS MATHEMATICS / Numerical Analysis Richrigkeit von Ergebnissen |
| TableOfContents | F The symmetric solution set -- G INTLAB -- Bibliography -- Symbol Index -- Author Index -- Subject Index Intro -- Preface -- Contents -- 1 Preliminaries -- 1.1 Notations and basic definitions -- 1.2 Metric spaces -- 1.3 Normed linear spaces -- 1.4 Polynomials -- 1.5 Zeros and fixed points of functions -- 1.6 Mean value theorems -- 1.7 Normal forms of matrices -- 1.8 Eigenvalues -- 1.9 Nonnegative matrices -- 1.10 Particular matrices -- 2 Real intervals -- 2.1 Intervals, partial ordering -- 2.2 Interval arithmetic -- 2.3 Algebraic properties, χ -function -- 2.4 Auxiliary functions -- 2.5 Distance and topology -- 2.6 Elementary interval functions -- 2.7 Machine interval arithmetic -- 3 Interval vectors, interval matrices -- 3.1 Basics -- 3.2 Powers of interval matrices -- 3.3 Particular interval matrices -- 4 Expressions, P-contraction, ε-inflation -- 4.1 Expressions, range -- 4.2 P-contraction -- 4.3 ε-inflation -- 5 Linear systems of equations -- 5.1 Motivation -- 5.2 Solution sets -- 5.3 Interval hull -- 5.4 Direct methods -- 5.5 Iterative methods -- 6 Nonlinear systems of equations -- 6.1 Newton method - one-dimensional case -- 6.2 Newton method - multidimensional case -- 6.3 Krawczyk method -- 6.4 Hansen-Sengupta method -- 6.5 Further existence tests -- 6.6 Bisection method -- 7 Eigenvalue problems -- 7.1 Quadratic systems -- 7.2 A Krawczyk-like method -- 7.3 Lohner method -- 7.4 Double or nearly double eigenvalues -- 7.5 The generalized eigenvalue problem -- 7.6 A method due to Behnke -- 7.7 Verification of singular values -- 7.8 An inverse eigenvalue problem -- 8 Automatic differentiation -- 8.1 Forward mode -- 8.2 Backward mode -- 9 Complex intervals -- 9.1 Rectangular complex intervals -- 9.2 Circular complex intervals -- 9.3 Applications of complex intervals -- Final Remarks -- Appendix -- A Jordan normal form -- B Brouwer's fixed point theorem -- C Theorem of Newton-Kantorovich -- D The row cyclic Jacobi method -- E The CORDIC Algorithm 1. Preliminaries -- C. Proof of the Newton–Kantorovich Theorem -- Contents -- 3. Interval vectors, interval matrices -- Subject Index Preface -- Final Remarks -- A. Proof of the Jordan normal form -- 2. Real intervals -- E. The CORDIC algorithm -- D. Convergence proof of the row cyclic Jacobi method -- F. The symmetric solution set – a proof of Theorem 5.2.6 -- 8. Automatic differentiation -- 4. Expressions, P-contraction, ε-inflation -- Bibliography -- G. A short introduction to INTLAB -- 6. Nonlinear systems of equations -- 9. Complex intervals -- 7. Eigenvalue problems and related ones -- Symbol Index -- B. Two elementary proofs of Brouwer’s fixed point theorem -- Author Index -- 5. Linear systems of equations -- Frontmatter -- Appendix -- |
| Title | Interval analysis : and automatic result verification |
| URI | https://cir.nii.ac.jp/crid/1130282269716705920 https://www.perlego.com/book/611302/interval-analysis-and-automatic-result-verification-pdf https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=4843236 https://www.degruyter.com/isbn/9783110499469 https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9783110498059 https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9783110499469&uid=none |
| Volume | 65 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3db9MwELdYeWEPfA1EB0MR4g0FEn-Hx5bChFSeBupbZMfOVK1KUZMObX89Z8dJ2mrSBC9WEjk-xT_rfJe7-xmh94zZlKjMxOAt45iy1MYKnLBYE04VWBiksM5RnP_g5z_p9wVbDEdw-eqSRn8sbu-sK_kfVOEZ4OqqZP8B2X5QeADXgC-0gDC0B8Zvfzsknm-ufZl_4BTxRcuOd3XbrDti5nq7aj7AR7lsoL2A-1zdtEh9c3HyybTqcnSD-5-KA_f_C6ylzfam69Y5hgR2debNjzvVJPOMEqEf-Dy0PS7lgHl6MsGOLBXjxRE6EgJ0xkPYK2fz4R-WJERg5kpmenktqdFwH3hNQeKnPXnH6FjVV6DIQck3Nezs1XIJPshvu1nZy_Wevf_4j88cMPay_dIdA-DiKRq5opBn6IGtnqMnwXSPgmKsTxDrEIk6RKLPcGmiHo-oxSPaxeMF-vV1djE9j8OJFLEiWUpErCm1SpSlTYrMBQJlaUpwYLlkVtqsUKWk0goDShTrBBvCudbcFuAUaFUYZshLNKrWlX2FIkp0orPExUEFpVhryYRRiaaOw89SNkbvdiYov1756Hmd97MowTK-t5Ob6jE6g8nNi6VrUxepBquQO-4wAUPgZIxOwrTn7dvcdxqjqMMg98OGdOF8NplSSQkmHMQfYJM7BpZ98af3iH-NHg0L-w0aNZutPQNLr9Fvw4L7C27WRbo |
| linkProvider | ProQuest Ebooks |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.title=Interval+analysis+%3A+and+automatic+result+verification&rft.au=Mayer%2C+G%C3%BCnter&rft.date=2017-01-01&rft.pub=De+Gruyter&rft.isbn=9783110500639&rft_id=info:doi/10.1515%2F9783110499469&rft.externalDocID=BB2352522X |
| thumbnail_l | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fwww.perlego.com%2Fbooks%2FRM_Books%2Fde_gruyter_frmluoo%2F9783110498059.jpg |
| thumbnail_m | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fwww.degruyter.com%2Fdocument%2Fcover%2Fisbn%2F9783110499469%2Foriginal http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fvle.dmmserver.com%2Fmedia%2F640%2F97831104%2F9783110498059.jpg http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fvle.dmmserver.com%2Fmedia%2F640%2F97831104%2F9783110499469.jpg |