Abstract
We study asymptotically fast multiplication algorithms for matrix pairs of arbitrary dimensions, and optimize the exponents of their arithmetic complexity bounds. For a large class of input matrix pairs, we improve the known exponents. We also show some applications of our results: (i) we decrease from O(n 2 + n 1+o(1)logq) to O(n 1.9998 + n 1+o(1)logq) the known arithmetic complexity bound for the univariate polynomial factorization of degree n over a finite field with q elements; (ii) we decrease from 2.837 to 2.7945 the known exponent of the work and arithmetic processor bounds for fast deterministic (NC) parallel evaluation of the determinant, the characteristic polynomial, and the inverse of an n × n matrix, as well as for the solution to a nonsingular linear system of n equations; (iii) we decrease from O(m 1.575 n) to O(m 1.5356 n) the known bound for computing basic solutions to a linear programming problem with m constraints and n variables.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
