The algebraic eigenvalue problem
The algebraic eigenvalue problem
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The Calculation of Multivariate Polynomial Resultants
Journal of the ACM (JACM)
An Assessment of Techniques for Proving Program Correctness
ACM Computing Surveys (CSUR)
The correctness of numerical algorithms
Proceedings of ACM conference on Proving assertions about programs
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
Perturbing numerical calculations for statistical analysis of floating-point program (in)stability
Proceedings of the 19th international symposium on Software testing and analysis
| Hi-index | 0.00 |
In this paper we will be concerned with portions of roundoff analysis which can be automated. Conditions are given under which proofs of numerical stability can be performed completely automatically and very economically (in particular, in polynomial time). We also discuss the use of “numerical heuristics” which apply “hill-climbing” methods to functionals measuring contamination from roundoff. In Section 2 we will relate this work to the extensive literature on roundoff error. Two properties of error propagation in straight-line programs are defined in Section 3, and their relationship demonstrated in Theorem 1. The properties are guaranteed to be effectively decidable since they can be formulated in the first-order theory of real-closed fields. In Section 4 we present sufficient conditions for the properties to hold; conditions which can be checked in time bounded by a polynomial in the size of the given straight-line program.