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Table Card RUSMARC
Title: De Gruyter studies in mathematics ;. Interval Analysis. — v. 65.
Creators: Mayer Günter.
Imprint: Berlin/Boston: De Gruyter, 2017
Collection: Электронные книги зарубежных издательств; Общая коллекция
Subjects: Interval analysis (Mathematics); MATHEMATICS / Applied; MATHEMATICS / Probability & Statistics / General; EBSCO eBooks
Document type: Other
File type: PDF
Language: English
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Record key: ocn985959592

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Table of Contents

  • 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
    • F The symmetric solution set
    • G INTLAB
  • Bibliography
  • Symbol Index
  • Author Index
  • Subject Index

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