Accurate Numerical Algorithms
Springer Berlin (Verlag)
978-3-540-51477-0 (ISBN)
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.
Erscheint lt. Verlag | 16.8.1989 |
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Reihe/Serie | Project 1072. DIAMOND | Research Reports Esprit |
Zusatzinfo | IX, 234 p. 6 illus. |
Verlagsort | Berlin |
Sprache | englisch |
Maße | 170 x 242 mm |
Gewicht | 450 g |
Themenwelt | Informatik ► Theorie / Studium ► Algorithmen |
Mathematik / Informatik ► Mathematik ► Algebra | |
Mathematik / Informatik ► Mathematik ► Analysis | |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
Schlagworte | Accurate Arithmetic • Algorithm analysis and problem complexity • eigenvalue problems • Eigenwertprobleme • Nicht-lineare Systeme • Nonlinear Systems • Numerical analysis • Numerische Analysis • Selbstvalidierende Algorithmen • Self-Validating Algorithms • wissenschaftliches Rechnen |
ISBN-10 | 3-540-51477-5 / 3540514775 |
ISBN-13 | 978-3-540-51477-0 / 9783540514770 |
Zustand | Neuware |
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