Accurate Numerical Algorithms: A Collection of Research Papers (Research Reports Esprit / Project 1072. D.I.A.M.O.N.D.): 1 - Brossura

 
9783540514770: Accurate Numerical Algorithms: A Collection of Research Papers (Research Reports Esprit / Project 1072. D.I.A.M.O.N.D.): 1
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ISBN 10: 3540514775 ISBN 13: 9783540514770
Casa editrice: Springer-Verlag, 1989

Sinossi

The major goals of the Esprit Project 1072, D.I.A.M.O.N.D. (Development and Integration of Accurate Mathematical Operations in Numerical Data-Processing), were to develop a set of accurate numerical algorithms (work package 3) and to provide tools to support the

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Contenuti

Highly Accurate Numerical Algorithms.- 0. Introduction.- 1. Design of E-Methods.- 2. Application of Brouwer’s Fixed-Point Theorem.- 3. Eigenvalues.- 4. The Application of Theorems on Zeros in the Complex Plane.- 5. Linear Systems for Sparse Matrices.- 6. Quadrature.- 7. Nonlinear Systems.- References.- Appendix. The PASCAL-SC Demonstration Package.- Solving the Complex Algebraic Eigenvalue Problem with Verified High Accuracy.- 1. Introduction.- 2. Mathematical Foundations.- 3. Inclusion of the Complex Algebraic Eigenvalue Problem.- 4. The Inclusion Algorithm.- References.- Techniques for Generating Accurate Eigensolutions in ADA.- 1. Introduction.- 2. Method.- 3. Implementation.- 4. Appendix.- 5. Glossary.- References.- Enclosing all Eigenvalues of Symmetric Matrices.- 1. Introduction.- 2. Simple Method for Computing Enclosures of Eigenvalues.- 3. Computing Eigenvector Approximations with High Accuracy.- 4. Computing Eigenvalue Enclosures with High Accuracy.- 5. Computing Eigenvector Enclosures.- 6. Numerical Examples.- References.- Computing Accurate Eigenvalues of a Hermitian Matrix.- 1. Introduction.- 2. A Jacobi Method for the Hermitian Eigenvalue Problem.- 3. Inclusion of the Estimated Eigenvalues.- 4. Improvement of the Eigensolution by Newton Iterations.- 5. Adapting the Algorithm to Ada.- 6. Ada Package Specification.- 7. Test Results.- 8. Conclusions.- References.- Verified Inclusion of all Roots of a Complex Polynomial by means of Circular Arithmetic.- 1. Introduction.- 2. Refinement of the Schur/Cohn Algorithm.- 3. Refined Bisecting Process.- 4. Solving Algorithm.- 5. Performance, Example.- 6. Conclusions.- Literature.- Verified Results for Linear Systems with Sparse Matrices.- 1. Introduction.- 2. Method Description.- 3. Method Implementation.- 4. Remarks.- References.- Self-Validating Numerical Quadrature.- 1. Review.- 2. Fundamentals.- 3. Verified Computation of the Procedure Error via Automatic Differentiation.- 4. Numerical Quadrature via Modified Romberg-Extrapolation.- 5. Faster Reduction of the Total Error via Adaptive Refinement.- 6. Numerical Results.- References.- Solving Nonlinear Equations with Verification of Results.- 1. Introduction.- 2. Inclusion of Zeros.- 3. Numerical Problems with Traditional Methods.- 4. Improvement of Theoretical Behaviour of Traditional Methods.- 5. Condition of a System of Nonlinear Equations.- 6. Implementation Aspects.- References.

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Editore
Springer-Verlag
Data di pubblicazione
1989
Lingua
Inglese
ISBN 10 
3540514775
ISBN 13 
9783540514770
Rilegatura
Copertina flessibile
Numero di pagine
248
Redattore
Ullrich Christian
Contatto del produttore
non disponibile
Persona responsabile
CMN Printpool Inh. Mathis Neumann
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Hamburg
Germania

Altre edizioni note dello stesso titolo

9780387514772: Accurate Numerical Algorithms: A Collection of Research Papers

Edizione in evidenza

ISBN 10:  0387514775 ISBN 13:  9780387514772
Casa editrice: Springer Verlag, 1989
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