2 research outputs found
Computational Complexity and Numerical Stability of Linear Problems
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.Comment: 16 pages; updated to reflect referees' remarks; to appear in
Proceedings of the 5th European Congress of Mathematic
Computational Complexity and Numerical Stability of Linear Problems
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.Comment: 16 pages; updated to reflect referees' remarks; to appear in
Proceedings of the 5th European Congress of Mathematic