Methods and Applications of Error-Free Computation

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.