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Title: A new approach to parallel computation of polynomial GCD and to related parallel computations over fields and integer rings

Abstract

We devise effective randomized parallel algorithms for the solution (over any field and some integers rings of constants) of several fundamental problems of computations with polynomials and structured matrices, well known for their resistance to effective parallel solution. This includes computing the gcd of two polynomials, as well as any selected entry of the extended Euclidean scheme for these polynomials and of Pade approximation table, the solution of the Berlekamp-Massey problem of recovering the coefficients of a linear recurrence from its terms, the solution of a nonsingular Toeplitz linear system of equations, computing the ranks of Toephtz matrices, and other related computations with Toeplitz, Hankel, Vandermonde, Cauchy (generalized Hilbert) matrices and with matrices having similar structures. Our algorithms enable us to reach new record estimates for randomized parallel arithmetic complexity of these computations, that is, O((log n){sup 3}) time and O ((n{sup 2} log log n) / (log n){sup 2}) arithmetic processors, n being the input size. The results have further applications to numerous related computations over abstract fields.

Authors:
 [1]
  1. Lehman College, Bronx, NY (United States)
Publication Date:
OSTI Identifier:
416837
Report Number(s):
CONF-960121-
CNN: Grant CCR 9020690; TRN: 96:005887-0060
Resource Type:
Conference
Resource Relation:
Conference: 7. annual ACM-SIAM symposium on discrete algorithms, Atlanta, GA (United States), 28-30 Jan 1996; Other Information: PBD: 1996; Related Information: Is Part Of Proceedings of the seventh annual ACM-SIAM symposium on discrete algorithms; PB: 596 p.
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; POLYNOMIALS; ALGORITHMS; MATRICES; RANDOMNESS; PARALLEL PROCESSING

Citation Formats

Pan, V Y. A new approach to parallel computation of polynomial GCD and to related parallel computations over fields and integer rings. United States: N. p., 1996. Web.
Pan, V Y. A new approach to parallel computation of polynomial GCD and to related parallel computations over fields and integer rings. United States.
Pan, V Y. 1996. "A new approach to parallel computation of polynomial GCD and to related parallel computations over fields and integer rings". United States.
@article{osti_416837,
title = {A new approach to parallel computation of polynomial GCD and to related parallel computations over fields and integer rings},
author = {Pan, V Y},
abstractNote = {We devise effective randomized parallel algorithms for the solution (over any field and some integers rings of constants) of several fundamental problems of computations with polynomials and structured matrices, well known for their resistance to effective parallel solution. This includes computing the gcd of two polynomials, as well as any selected entry of the extended Euclidean scheme for these polynomials and of Pade approximation table, the solution of the Berlekamp-Massey problem of recovering the coefficients of a linear recurrence from its terms, the solution of a nonsingular Toeplitz linear system of equations, computing the ranks of Toephtz matrices, and other related computations with Toeplitz, Hankel, Vandermonde, Cauchy (generalized Hilbert) matrices and with matrices having similar structures. Our algorithms enable us to reach new record estimates for randomized parallel arithmetic complexity of these computations, that is, O((log n){sup 3}) time and O ((n{sup 2} log log n) / (log n){sup 2}) arithmetic processors, n being the input size. The results have further applications to numerous related computations over abstract fields.},
doi = {},
url = {https://www.osti.gov/biblio/416837}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Dec 31 00:00:00 EST 1996},
month = {Tue Dec 31 00:00:00 EST 1996}
}

Conference:
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