Chapter 10: Algebraic Algorithms

Abstract

Our Chapter in the upcoming Volume I: Computer Science and Software Engineering of Computing Handbook (Third edition), Allen Tucker, Teo Gonzales and Jorge L. Diaz-Herrera, editors, covers Algebraic Algorithms, both symbolic and numerical, for matrix computations and root-finding for polynomials and systems of polynomials equations. We cover part of these large subjects and include basic bibliography for further study. To meet space limitation we cite books, surveys, and comprehensive articles with pointers to further references, rather than including all the original technical papers.

41.1 pages

References in corpus (6)

• Group-theoretic algorithms for matrix multiplication
• Stable normal forms for polynomial system solving
• The DMM bound: multivariate (aggregate) separation bounds
• Randomized Matrix Computations
• Random polynomials and expected complexity of bisection methods for real solving
• Improved complexity bounds for real root isolation using Continued Fractions