Toward Abstract Numerical Analysis
- 1 July 1973
- journal article
- Published by Association for Computing Machinery (ACM) in Journal of the ACM
- Vol. 20 (3) , 399-408
- https://doi.org/10.1145/321765.321772
Abstract
This paper deals with a technique for proving that certain problems of numerical analysis are numerically unsolvable. So that only methods which are natural for dealing with analytic problems may be presented, notions from recursive function theory have been avoided. Instead, the number of necessary function evaluations is taken as the measure of computational complexity. The role of topological concepts in the study of computability is examined. Last, a topological result is used to prove that a simple initial-value problem is numerically unsolvable.Keywords
This publication has 3 references indexed in Scilit:
- The concept of effective method applied to computational problems of linear algebraJournal of Computer and System Sciences, 1971
- The primitive recursive analysis of ordinary differential equations and the complexity of their solutionsJournal of Computer and System Sciences, 1969
- Analysis in the Computable Number FieldJournal of the ACM, 1968