Zobrazeno 1 - 10
of 41
pro vyhledávání: '"Alkiviadis G. Akritas"'
Given the polynomials f, g ∈ Z[x] the main result of our paper,Theorem 1, establishes a direct one-to-one correspondence between the modified Euclidean and Euclidean polynomial remainder sequences (prs’s) of f, gcomputed in Q[x], on one hand, and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::68b4218eeb4a30d72e8b3656501760fc
https://hdl.handle.net/10525/2913
https://hdl.handle.net/10525/2913
In this paper we present two new methods for computing the subresultant polynomial remainder sequence (prs) of two polynomials f, g ∈ Z[x]. We are now able to also correctly compute the Euclidean and modified Euclidean prs of f, g by using either o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4d0ba75630ce88bcd72d66373e1f530b
https://hdl.handle.net/10525/2924
https://hdl.handle.net/10525/2924
Autor:
Alkiviadis G. Akritas
Publikováno v:
Journal of Mathematical Sciences. 168:309-325
In this paper, we present two different versions of Vincent’s theorem of 1836 and discuss various real root isolation methods derived from them: one using continued fractions and two using bisections, the former being the fastest real root isolatio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5337ff49f90a296e18a07f1e65144ba2
https://doi.org/10.1007/s10958-010-9982-1
https://doi.org/10.1007/s10958-010-9982-1
Publikováno v:
Nonlinear Analysis, Vol 13, Iss 3 (2008)
In this paper we compare four implementations of the Vincent-AkritasStrzebo´nski Continued Fractions (VAS-CF) real root isolation method using four different (two linear and two quadratic complexity) bounds on the values of the positive roots of pol
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::014c9e1ddcd0201ef224dd438a3b6a95
https://doi.org/10.15388/na.2008.13.3.14557
https://doi.org/10.15388/na.2008.13.3.14557
Publikováno v:
Nonlinear Analysis, Vol 11, Iss 2 (2006)
Given an m × n matrix A, with m ≥ n, the four subspaces associated with it are shown in Fig. 1 (see [1]). Fig. 1. The row spaces and the nullspaces of A and AT; a1 through an and h1 through hm are abbreviations of the alignerframe and hangerframe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cd9092cd734da7d3e6137ba8f0e4389f
https://doi.org/10.15388/na.2006.11.2.14753
https://doi.org/10.15388/na.2006.11.2.14753
Publikováno v:
Nonlinear Analysis, Vol 10, Iss 4 (2005)
Recent progress in polynomial elimination has rendered the computation of the real roots of ill-conditioned polynomials of high degree (over 1000) with huge coefficients (several thousand digits) a critical operation in computer algebra. To rise to t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4d4dc534616fba058eefe9860957384f
https://doi.org/10.15388/na.2005.10.4.15110
https://doi.org/10.15388/na.2005.10.4.15110
Publikováno v:
Mathematics and Computers in Simulation. 67:15-31
Let A be an m×n matrix with m≥n. Then one form of the singular-value decomposition of A is A=U T ΣV, where U and V are orthogonal and Σ is square diagonal. That is, UUT=Irank(A), VVT=Irank(A), U is rank(A)×m, V is rank(A)×n and Σ= σ 1 0 ⋯
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::78d0467cb96b14f323b671f2abb16fe3
https://doi.org/10.1016/j.matcom.2004.05.005
https://doi.org/10.1016/j.matcom.2004.05.005
Publikováno v:
Mathematics and Computers in Simulation. 42:585-593
Despite the fact that the importance of Sylvester's determinant identity has been recognized in the past, we were able to find only one proof of it in English (Bareiss, 1968), with reference to some others. (Recall that Sylvester (1857) stated this t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::211947bae1af213deeccc073399f6dc3
https://doi.org/10.1016/s0378-4754(96)00035-3
https://doi.org/10.1016/s0378-4754(96)00035-3
Publikováno v:
Reliable Computing. 1:375-381
We present an improved variant of the matrix-triangularization subresultant prs method [1] for the computation of a greatest common divisor of two polynomialsA andB (of degreesm andn, respectively) along with their polynomial remainder sequence. It i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8823af4e2f1597dc7dba70de030dadd8
https://doi.org/10.1007/bf02391682
https://doi.org/10.1007/bf02391682
In this paper we present F LQ, a quadratic complexity bound on the values of the positive roots of polynomials. This bound is an extension of FirstLambda, the corresponding linear complexity bound and, consequently, it is derived from Theorem 3 below
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e6a0f38668cf597ec11ef8a53cba5f1b
https://hdl.handle.net/10525/380
https://hdl.handle.net/10525/380