Coverart for item
The Resource Interval Analysis : and Automatic Result Verification, Günter Mayer

Interval Analysis : and Automatic Result Verification, Günter Mayer

Label
Interval Analysis : and Automatic Result Verification
Title
Interval Analysis
Title remainder
and Automatic Result Verification
Statement of responsibility
Günter Mayer
Creator
Author
Subject
Language
eng
Summary
  • 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, [epsilon]-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
Member of
Cataloging source
DEGRU
http://library.link/vocab/creatorName
Mayer, G.
Dewey number
510
Index
index present
Language note
In English
LC call number
QA297.75
LC item number
.M39 2017
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
De Gruyter Studies in Mathematics
Series volume
65
http://library.link/vocab/subjectName
  • Interval analysis (Mathematics)
  • MATHEMATICS
  • Interval analysis (Mathematics)
  • Calcul sur des intervalles
Label
Interval Analysis : and Automatic Result Verification, Günter Mayer
Instantiates
Publication
Copyright
Bibliography note
Includes bibliographical references (pages 483-498) and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 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
  • Frontmatter
  • Preface
  • Contents
  • 1. Preliminaries
  • 2. Real intervals
  • 3. Interval vectors, interval matrices
  • 4. Expressions, P-contraction, [epsilon]-inflation
  • 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
  • 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
Control code
984647843
Extent
1 online resource (532 pages)
Form of item
online
Isbn
9783110500639
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
  • 10.1515/9783110499469
  • 9783110499469
  • urn:nbn:de:101:1-201704192952
  • 9783110498059
  • urn:nbn:de:101:1-201706141932
  • 40027155563
http://library.link/vocab/ext/overdrive/overdriveId
1006393
Specific material designation
remote
System control number
(OCoLC)984647843
Label
Interval Analysis : and Automatic Result Verification, Günter Mayer
Publication
Copyright
Bibliography note
Includes bibliographical references (pages 483-498) and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 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
  • Frontmatter
  • Preface
  • Contents
  • 1. Preliminaries
  • 2. Real intervals
  • 3. Interval vectors, interval matrices
  • 4. Expressions, P-contraction, [epsilon]-inflation
  • 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
  • 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
Control code
984647843
Extent
1 online resource (532 pages)
Form of item
online
Isbn
9783110500639
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
  • 10.1515/9783110499469
  • 9783110499469
  • urn:nbn:de:101:1-201704192952
  • 9783110498059
  • urn:nbn:de:101:1-201706141932
  • 40027155563
http://library.link/vocab/ext/overdrive/overdriveId
1006393
Specific material designation
remote
System control number
(OCoLC)984647843

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