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161.
Yixun Shi 《Numerical Linear Algebra with Applications》2002,9(3):195-203
This paper studies the possibility of combining interior point strategy with a steepest descent method when solving convex programming problems, in such a way that the convergence property of the interior point method remains valid but many iterations do not request the solution of a system of equations. Motivated by this general idea, we propose a hybrid algorithm which combines a primal–dual potential reduction algorithm with the use of the steepest descent direction of the potential function. The complexity of the potential reduction algorithm remains valid but the overall computational cost can be reduced. Our numerical experiments are also reported. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
162.
We describe algorithms for polynomial factorization over the binary field , and their implementation. They allow polynomials of degree up to to be factored in about one day of CPU time, distributing the work on two processors.
163.
We give an analogue of Levin–Sodin–Yuditskii's study of the dynamical Ruelle determinants of hyperbolic rational maps in the case of subhyperbolic quadratic polynomials. Our main tool is to reduce to an expanding situation. We do so by applying a dynamical change of coordinates on the domains of a Markov partition constructed from the landing ray at the postcritical repelling orbit. We express the dynamical determinants
as the product of an (entire) determinant with an explicit expression involving the postcritical repelling orbit, thus explaining the poles in d
(z). 相似文献
164.
We study trigonometric sums in finite fields
. The Weil estimate of such sums is well known:
, where f is a polynomial with coefficients from F(Q). We construct two classes of polynomials f,
, for which
attains the largest possible value and, in particular,
. 相似文献
165.
In this paper we present an algorithm for recursively generating orthogonal bivariate polynomials on a discrete set S 2. For this purpose we employ commuting pairs of real symmetric matrices H, K
n×n
to obtain, in a certain sense, a two dimensional Hermitian Lanczos method. The resulting algorithm relies on a recurrence having a slowly growing length. Practical implementation issues an applications are considered. The method can be generalized to compute orthogonal polynomials depending on an arbitrary number of variables. 相似文献
166.
Moharram A. Khan 《Czechoslovak Mathematical Journal》2002,52(2):401-413
Let p, q and r be fixed non-negative integers. In this note, it is shown that if R is left (right) s-unital ring satisfying
, respectively) where
, then R is commutative. Moreover, commutativity of R is also obtained under different sets of constraints on integral exponents. Also, we provide some counterexamples which show that the hypotheses are not altogether superfluous. Thus, many well-known commutativity theorems become corollaries of our results. 相似文献
167.
We compute renormalization-group fixed points and their spectrum in an ultralocal approximation. We study a case of two competing nontrivial fixed points for a three-dimensional real N-component field: the O(N)-invariant fixed point vs. the cubic-invariant fixed point. We compute the critical value N
c of the cubic
4-perturbation at the O(N)-fixed point. The O(N)-fixed point is stable under a cubic
4-perturbation below N
c; above N
c it is unstable. The Critical value comes out as 2.219435<N
c<2.219436 in the ultralocal approximation. We also compute the critical value of N at the cubic invariant fixed point. Within the accuracy of our computations, the two values coincide. 相似文献
168.
Zeng Guangxing 《中国科学A辑(英文版)》1999,42(3):272-280
For an ordered field (K,T) and an idealI of the polynomial ring
, the construction of the generalized real radical
ofI is investigated. When (K,T) satisfies some computational requirements, a method of computing
is presented.
Project supported by the National Natural Science Foundation of China (Grant No. 19661002) and the Climbing Project. 相似文献
169.
The multiplicities a of simple modules L in the composition series of Kac modules V lambda for the Lie superalgebra
(m/n ) were described by Serganova, leading to her solution of the character problem for
(m/n ). In Serganova's algorithm all with nonzero a are determined for a given this algorithm, turns out to be rather complicated. In this Letter, a simple rule is conjectured to find all nonzero a for any given weight . In particular, we claim that for an r-fold atypical weight there are 2r distinct weights such that a = 1, and a = 0 for all other weights . Some related properties on the multiplicities a are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan–Lusztig polynomials is discussed. 相似文献
170.
TZEKIS P.; KARAMPETAKIS N. P.; VARDULAKIS A. I. 《IMA Journal of Mathematical Control and Information》1999,16(4):391-401
The main purpose of this paper is to determine two new algorithmsfor the division of the polynomial matrix B(s) R[s]pxq by A(s) R[s]pxp (a) based on the Laurent matrix expansion at s = =of the inverse of A(s), i.e. A(s)1, and (b) in a waysimilar to the one presented by Gantmacher (1959). 相似文献