Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Analysis in the Computable Number Field
Journal of the ACM (JACM)
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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.