by Chong-kan Chiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 97-103). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Related Work --- p.2 / Chapter 1.2 --- Organizations of the Dissertation --- p.4 / Chapter 1.3 --- Notations --- p.4 / Chapter 2 --- Overview of ICLP(R) --- p.6 / Chapter 2.1 --- Basics of Interval Arithmetic --- p.6 / Chapter 2.2 --- Relational Interval Arithmetic --- p.8 / Chapter 2.2.1 --- Interval Reduction --- p.8 / Chapter 2.2.2 --- Arithmetic Primitives --- p.10 / Chapter 2.2.3 --- Interval Narrowing and Interval Splitting --- p.13 / Chapter 2.3 --- Syntax and Semantics --- p.16 / Chapter 3 --- Limitations of Interval Narrowing --- p.18 / Chapter 3.1 --- Computation Inefficiency --- p.18 / Chapter 3.2 --- Inability to Detect Inconsistency --- p.23 / Chapter 3.3 --- The Newton Language --- p.27 / Chapter 4 --- Design of CIAL --- p.30 / Chapter 4.1 --- The CIAL Architecture --- p.30 / Chapter 4.2 --- The Inference Engine --- p.31 / Chapter 4.2.1 --- Interval Variables --- p.31 / Chapter 4.2.2 --- Extended Unification Algorithm --- p.33 / Chapter 4.3 --- The Solver Interface and Constraint Decomposition --- p.34 / Chapter 4.4 --- The Linear and the Non-linear Solvers --- p.37 / Chapter 5 --- The Linear Solver --- p.40 / Chapter 5.1 --- An Interval Gaussian Elimination Solver --- p.41 / Chapter 5.1.1 --- Naive Interval Gaussian Elimination --- p.41 / Chapter 5.1.2 --- Generalized Interval Gaussian Elimination --- p.43 / Chapter 5.1.3 --- Incrementality of Generalized Gaussian Elimination --- p.47 / Chapter 5.1.4 --- Solvers Interaction --- p.50 / Chapter 5.2 --- An Interval Gauss-Seidel Solver --- p.52 / Chapter 5.2.1 --- Interval Gauss-Seidel Method --- p.52 / Chapter 5.2.2 --- Preconditioning --- p.55 / Chapter 5.2.3 --- Increment ality of Preconditioned Gauss-Seidel Method --- p.58 / Chapter 5.2.4 --- Solver Interaction --- p.71 / Chapter 5.3 --- Comparisons --- p.72 / Chapter 5.3.1 --- Time Complexity --- p.72 / Chapter 5.3.2 --- Storage Complexity --- p.73 / Chapter 5.3.3 --- Others --- p.74 / Chapter 6 --- Benchmarkings --- p.76 / Chapter 6.1 --- Mortgage --- p.78 / Chapter 6.2 --- Simple Linear Simultaneous Equations --- p.79 / Chapter 6.3 --- Analysis of DC Circuit --- p.80 / Chapter 6.4 --- Inconsistent Simultaneous Equations --- p.82 / Chapter 6.5 --- Collision Problem --- p.82 / Chapter 6.6 --- Wilkinson Polynomial --- p.85 / Chapter 6.7 --- Summary and Discussion --- p.86 / Chapter 6.8 --- Large System of Simultaneous Equations --- p.87 / Chapter 6.9 --- Comparisons Between the Incremental and the Non-Incremental Preconditioning --- p.89 / Chapter 7 --- Concluding Remarks --- p.93 / Chapter 7.1 --- Summary and Contributions --- p.93 / Chapter 7.2 --- Future Work --- p.95 / Bibliography --- p.97
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_320690 |
| Date | January 1994 |
| Contributors | Chiu, Chong-kan., Chinese University of Hong Kong Graduate School. Division of Computer Science. |
| Publisher | Chinese University of Hong Kong |
| Source Sets | The Chinese University of Hong Kong |
| Language | English |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, xii, 103 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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