Ebook: Validation Numerics: Theory and Applications

The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.

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The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.

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The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.
Content:
Front Matter....Pages i-ix
On a Unified Concept of Mathematics....Pages 1-10
A General Approach to a Class of Single-Step Methods for the Simultaneous Inclusion of Polynomial Zeros....Pages 11-19
On Some Properties of an Interval Newton Type Method and its Modification....Pages 21-32
Verified Solution of the Integral Equations for the Two-Dimensional Dirichlet and Neumann Problem....Pages 33-43
Two-Stage Interval Iterative Methods....Pages 45-65
Convergence Acceleration for Some Rootfinding Methods....Pages 67-78
A Program for Enclosing Cumulative Binomial Probabilities....Pages 79-92
Effective Evaluation of Hausdorff Distances for Finite Unions of Hyperrectangles....Pages 93-100
A Verified Computation of Fourier-Representations of Solutions for Functional Equations....Pages 101-115
The Cluster Problem in Global Optimization: the Univariate Case....Pages 117-127
Developing Expert Systems for Validating Numerics....Pages 129-146
Computation of Interval Bounds for Weierstrass’ Elliptic Function ?(z)....Pages 147-159
Solving Nonlinear Elliptic Problems with Result Verification Using an H -1 Type Residual Iteration....Pages 161-173
The Wrapping Effect, Ellipsoid Arithmetic, Stability and Confidence Regions....Pages 175-190
Validated Solution of Large Linear Systems....Pages 191-212
The Interval Buneman Algorithm for Arbitrary Block Dimension....Pages 213-231
On the Existence and the Verified Determination of Homoclinic and Heteroclinic Orbits of the Origin for the Lorenz Equations....Pages 233-246
Verification in Computer Algebra Systems....Pages 247-263
FORTRAN-XSC A Portable Fortran 90 Module Library for Accurate and Reliable Scientific Computing....Pages 265-285
Implementation of Accurate Matrix Multiplication on the CM-2....Pages 287-291

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The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.
Content:
Front Matter....Pages i-ix
On a Unified Concept of Mathematics....Pages 1-10
A General Approach to a Class of Single-Step Methods for the Simultaneous Inclusion of Polynomial Zeros....Pages 11-19
On Some Properties of an Interval Newton Type Method and its Modification....Pages 21-32
Verified Solution of the Integral Equations for the Two-Dimensional Dirichlet and Neumann Problem....Pages 33-43
Two-Stage Interval Iterative Methods....Pages 45-65
Convergence Acceleration for Some Rootfinding Methods....Pages 67-78
A Program for Enclosing Cumulative Binomial Probabilities....Pages 79-92
Effective Evaluation of Hausdorff Distances for Finite Unions of Hyperrectangles....Pages 93-100
A Verified Computation of Fourier-Representations of Solutions for Functional Equations....Pages 101-115
The Cluster Problem in Global Optimization: the Univariate Case....Pages 117-127
Developing Expert Systems for Validating Numerics....Pages 129-146
Computation of Interval Bounds for Weierstrass’ Elliptic Function ?(z)....Pages 147-159
Solving Nonlinear Elliptic Problems with Result Verification Using an H -1 Type Residual Iteration....Pages 161-173
The Wrapping Effect, Ellipsoid Arithmetic, Stability and Confidence Regions....Pages 175-190
Validated Solution of Large Linear Systems....Pages 191-212
The Interval Buneman Algorithm for Arbitrary Block Dimension....Pages 213-231
On the Existence and the Verified Determination of Homoclinic and Heteroclinic Orbits of the Origin for the Lorenz Equations....Pages 233-246
Verification in Computer Algebra Systems....Pages 247-263
FORTRAN-XSC A Portable Fortran 90 Module Library for Accurate and Reliable Scientific Computing....Pages 265-285
Implementation of Accurate Matrix Multiplication on the CM-2....Pages 287-291
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