Computational Complexity and Numerical Stability of Linear Problems

Details Computational Complexity and Numerical Stability of Linear Problems Computational Complexity and Numerical Stability of Linear Problems

2009-06-03

arxiv.org/abs/0906.0687v2

European Congress of Mathematics Amsterdam, 14-18 July, 2008, EMS Publishing House, pp. 381-400

Computer Science

Computational Complexity

16 pages; updated to reflect referees' remarks; to appear in Proceedings of the 5th European Congress of Mathematics

Scientific paper

10.4171/077-1/16

We survey classical and recent developments in numerical linear algebra, focusing on two issues: computational complexity, or arithmetic costs, and numerical stability, or performance under roundoff error. We present a brief account of the algebraic complexity theory as well as the general error analysis for matrix multiplication and related problems. We emphasize the central role played by the matrix multiplication problem and discuss historical and modern approaches to its solution.

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