Methods and Applications of Error-Free Computation
Springer-Verlag New York Inc.
978-1-4612-9754-3 (ISBN)
I Residue or Modular Arithmetic.- 1. Introduction.- 2. Single-Modulus Residue Arithmetic.- 3. Multiple-Modulus Residue Arithmetic.- 4. Mapping Standard Residue Representations onto Integers.- 5. Single-Modulus Residue Arithmetic with Rational Numbers.- 6. The Forward Mapping and the Inverse Mapping.- 7. Multiple-Modulus Residue Arithmetic with Rational Numbers.- II Finite-Segment p-adic Arithmetic.- 1. Introduction.- 2. The Field of p-adic Numbers.- 3. Arithmetic in Qp.- 4. A Finite-Segment p-adic Number System.- 5. Arithmetic Operations on Hensel Codes.- 6. Removing a Leading Zero from a Hensel Code.- 7. Mapping a Hensel Code onto a Unique Order-N Farey Fraction.- III Exact Computation of Generalized Inverses.- 1. Introduction.- 2. Properties of g-inverses.- 3. Applications of g-inverses.- 4. Exact Computation of A+ if A Is a Rational Matrix.- 5. Failures of Residue Arithmetic and Precautionary Measures.- IV Integer Solutions to Linear Equations.- 1. Introduction.- 2. Theoretical Background.- 3. The Matrix Formulation of Chemical Equations.- 4. Solving the Homogeneous System.- 5. Solving a Non-Homogeneous System.- 6. Solving Interval Linear Programming Problems.- 7. The Solution of Systems of Mixed-Integer Linear Equations.- V Iterative Matrix Inversion and the Iterative Solution of Linear Equations.- 1. Introduction.- 2. The Newton-Schultz Method for the Matrix Inverse.- 3. Iterative Solution of a Linear System.- 4. Iterative Computation of g-inverses.- VI The Exact Computation of the Characteristic Polynomial of a Matrix.- 1. Introduction.- 2. The Algorithm Applied to Lower Hessenberg Matrices.
Reihe/Serie | Monographs in Computer Science |
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Zusatzinfo | 194 p. |
Verlagsort | New York, NY |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Informatik ► Theorie / Studium ► Algorithmen |
Informatik ► Weitere Themen ► Hardware | |
Mathematik / Informatik ► Mathematik ► Analysis | |
Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
Schlagworte | Applications • Computation • Numerical analysis |
ISBN-10 | 1-4612-9754-0 / 1461297540 |
ISBN-13 | 978-1-4612-9754-3 / 9781461297543 |
Zustand | Neuware |
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