Interval methods for systems of equations
著者
書誌事項
Interval methods for systems of equations
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, 37）
Cambridge University Press, 1990
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注記
Bibliography: p. 231-248
Includes indexes
内容説明・目次
内容説明
An interval is a natural way of specifying a number that is specified only within certain tolerances. Interval analysis consists of the tools and methods needed to solve linear and nonlinear systems of equations in the presence of data uncertainties. Applications include the sensitivity analysis of solutions of equations depending on parameters, the solution of global nonlinear problems, and the verification of results obtained by finite-precision arithmetic. In this book emphasis is laid on those aspects of the theory which are useful in actual computations. On the other hand, the theory is developed with full mathematical rigour. In order to keep the book self-contained, various results from linear algebra (Perron-Frobenius theory, M- and H- matrices) and analysis (existence of solutions to nonlinear systems) are proved, often from a novel and more general viewpoint. An extensive bibliography is included.
目次
- Preface
- Symbol index
- 1. Basic properties of interval arithmetic
- 2. Enclosures for the range of a function
- 3. Matrices and sublinear mappings
- 4. The solution of square linear systems of equations
- 5. Nonlinear systems of equations
- 6. Hull computation
- References
- Author index
- Subject index.
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