Bibliography: p. 254-255.
|Statement||Edgar W. Kaucher, Willard L. Miranker.|
|Series||Notes and reports in computer science and applied mathematics ;, 9|
|Contributions||Miranker, Willard L.|
|LC Classifications||QA323 .K38 1984|
|The Physical Object|
|Pagination||xiii, 255 p. :|
|Number of Pages||255|
|LC Control Number||84003071|
Book Description: Self-Validating Numerics for Function Space Problems describes the development of computational methods for solving function space problems, including differential, integral, and function equations. This seven-chapter text highlights three approaches, namely, the E-methods, ultra-arithmetic, and computer arithmetic. Get this from a library! Self-validating numerics for function space problems: computation with guarantees for differential and integral equations. [Edgar W Kaucher; Willard L Miranker]. Self-Validating Numerics for Function Space Problems Computation with Guarantees for Differential and Integral Equations by Edgar W. Kaucher; Willard L. Miranker and Publisher Academic Press. Save up to 80% by choosing the eTextbook option for ISBN: , The print version of this textbook is ISBN: , Select Aspects of Self-Validating Numerics in Banach Spaces. Book chapter Full text access. of PDEs are transformed into a system of algebraic and/or ordinary differential equations which are expanded in the space coordinates. Hence, the original problem may be solved numerically or functionally in parallel for different space coordinates.
W e refer to such a computational environment as one which furnishes self-validating numerics. Here we provide a methodology for self-validating numerics for function space problems (e.g., differential equations, integral equations, functional equations,) (cf. [ 6 ]). The problem of validation of numerical computations turns out to involve fundamental interactions between computer arithmetics, programming languages, and mathematical algorithms. Details of these issues are examined, and examples of successful self-validating computational methods are given. E.W. Kaucher and W.L. Miranker, Self-Validating Numerics for Function Space Problems, Academic Press, New York, zbMATH Google Scholar. E. W. Kaucher and W. L. Miranker. — “Self validating numerics for function space problems”, Academic Press, New York, zbMATH Google Scholar.
This paper proposes a validation method for solutions of linear complementarity problems. The validation procedure consists of two sufficient conditions that can be tested on a digital computer. Hence i s a s o l u t i o n of (). Now we c o n s i d e r the i n i t i a l value problem (IVP) Aspects of Self-Validating Numerics in Banach Spaces u(0,x) = f(x) for (t.x) eD () for an a r b i t r a r y once c o n t i n u o u s l y d i f f e r e n t i a b l e function f: IR -. R. Author: Christian Ullrich Publisher: Academic Press ISBN: Size: MB Format: PDF, ePub, Docs View: Get Books Notes and Reports in Mathematics in Science and Engineering, Volume VII: Computer Arithmetic and Self-Validating Numerical Methods compiles papers presented at the first international conference on “Computer Arithmetic and Self-Validating Numerical Methods, . Self-Validating Numerics for Function Space Problems: Computation with Guarantees for Differential and Integral Equations (Notes and reports in computer science and applied mathematics) by Edgar W. Kaucher, Willard L. Miranker, Werner Rheinboldt.