Interval linear constraint solving in constraint logic programming.

by Chong-kan Chiu.Thesis (M.Phil.)--Chinese University of Hong Kong, 1994.Includes bibliographical references (leaves 97-103).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Related Work --- p.2Chapter 1.2 --- Organizations of the Dissertation --- p.4Chapter 1.3 --- Notations --- p.4Chapter 2 --- Overview of ICLP(R) --- p.6Chapter 2.1 --- Basics of Interval Arithmetic --- p.6Chapter 2.2 --- Relational Interval Arithmetic --- p.8Chapter 2.2.1 --- Interval Reduction --- p.8Chapter 2.2.2 --- Arithmetic Primitives --- p.10Chapter 2.2.3 --- Interval Narrowing and Interval Splitting --- p.13Chapter 2.3 --- Syntax and Semantics --- p.16Chapter 3 --- Limitations of Interval Narrowing --- p.18Chapter 3.1 --- Computation Inefficiency --- p.18Chapter 3.2 --- Inability to Detect Inconsistency --- p.23Chapter 3.3 --- The Newton Language --- p.27Chapter 4 --- Design of CIAL --- p.30Chapter 4.1 --- The CIAL Architecture --- p.30Chapter 4.2 --- The Inference Engine --- p.31Chapter 4.2.1 --- Interval Variables --- p.31Chapter 4.2.2 --- Extended Unification Algorithm --- p.33Chapter 4.3 --- The Solver Interface and Constraint Decomposition --- p.34Chapter 4.4 --- The Linear and the Non-linear Solvers --- p.37Chapter 5 --- The Linear Solver --- p.40Chapter 5.1 --- An Interval Gaussian Elimination Solver --- p.41Chapter 5.1.1 --- Naive Interval Gaussian Elimination --- p.41Chapter 5.1.2 --- Generalized Interval Gaussian Elimination --- p.43Chapter 5.1.3 --- Incrementality of Generalized Gaussian Elimination --- p.47Chapter 5.1.4 --- Solvers Interaction --- p.50Chapter 5.2 --- An Interval Gauss-Seidel Solver --- p.52Chapter 5.2.1 --- Interval Gauss-Seidel Method --- p.52Chapter 5.2.2 --- Preconditioning --- p.55Chapter 5.2.3 --- Increment ality of Preconditioned Gauss-Seidel Method --- p.58Chapter 5.2.4 --- Solver Interaction --- p.71Chapter 5.3 --- Comparisons --- p.72Chapter 5.3.1 --- Time Complexity --- p.72Chapter 5.3.2 --- Storage Complexity --- p.73Chapter 5.3.3 --- Others --- p.74Chapter 6 --- Benchmarkings --- p.76Chapter 6.1 --- Mortgage --- p.78Chapter 6.2 --- Simple Linear Simultaneous Equations --- p.79Chapter 6.3 --- Analysis of DC Circuit --- p.80Chapter 6.4 --- Inconsistent Simultaneous Equations --- p.82Chapter 6.5 --- Collision Problem --- p.82Chapter 6.6 --- Wilkinson Polynomial --- p.85Chapter 6.7 --- Summary and Discussion --- p.86Chapter 6.8 --- Large System of Simultaneous Equations --- p.87Chapter 6.9 --- Comparisons Between the Incremental and the Non-Incremental Preconditioning --- p.89Chapter 7 --- Concluding Remarks --- p.93Chapter 7.1 --- Summary and Contributions --- p.93Chapter 7.2 --- Future Work --- p.95Bibliography --- p.9