巧用换元法解代数题

换元法是代数处理方法中的最为基础的方法,在此总结出自身换元法、局部换元法等方法并用以解决一些所谓的难题,特别是数学竞赛题.

嵌套简单ILU分解代数预处理方法

In this paper, we propose a nested simple incomplete LU decomposition (NSILU) method for preconditioning iterative methods for solving largely scale and sparse ill-conditioned hnear systems. NSILU consists of some numerical techniques such as simple modification of Schur complement, compression of ill-condition structure by permutation, nested simple ILU, and inner-outer iteration. We give detailed error analysis of NSILU and estimations of condition number of the preconditioned coefficient matrix, together with numerical comparisons. We also show an analysis of inner accuracy strategies for the inner-outer iteration approach. Our new approach NSILU is very efficient for linear systems from a kind of two-dimensional nonlinear energy equations with three different temperature variables, where most of the calculations centered around solving large number of discretized and illconditioned linear systems in large scale. Many numerical experiments are given and compared in costs of flops, CPU times, and storages to show the efficiency and effectiveness of the NSILU preconditioning method. Numerical examples include middle-scale real matrices of size n = 3180 or n = 6360, a real apphcation of solving about 755418 linear systems of size n = 6360, and a simulation of order n=814080 with structures and properties similar as the real ones.

基于Legendre多项式的代数信号处理模型

在代数信号处理中可以定义不同的平移算子,建立不同的信号模型,每个信号模型有其对应的滤波,卷积,谱,傅里叶变换等相关的信号处理概念.文中定义了一种新的平移算子,基于该平移算子建立了基于Legendre正交多项式的无限1-D Legendre信号模型和有限1-D Legendre信号模型,并给出了该模型中傅里叶变换,谱以及频率响应等的具体概念.

Spectral Analysis for HSS Preconditioners

In this paper,we are interested in HSS preconditioners for saddle point lin- ear systems with a nonzero(2,2)-th block.We study an approximation of the spectra of HSS preconditioned matrices and use these results to illustrate and explain the spectra obtained from numerical examples,where the previous spectral analysis of HSS precon- ditioned matrices does not cover.

PARALLEL REGION PRESERVING MULTISECTION METHOD FOR SOLVING GENERALIZED EIGENPROBLEM

The parallel multisection method for solving algebraic eigenproblem has been presented in recent years with the development of the parallel computers, but all the research work is limited in standard eigenproblems of symmetric tridiagonal matrix. The multisection method for solving the generalized eigenproblem applied significantly in many science and engineering domains has not been studied. The parallel region preserving multisection method (PRM for short) for solving generalized eigenproblems of large sparse and real symmetric matrix is presented in this paper. This method not only retains the advantages of the conventional determinant search method (DS for short), but also overcomes its disadvantages such as leaking roots and disconvergence. We have tested the method on the YH 1 vector computer, and compared it with the parallel region preserving determinant search method the parallel region preserving bisection method (PRB for short). The numerical results show that PRM has a higher speed up, for instance, it attains the speed up of 7.7 when the scale of the problem is 2 114 and the eigenpair found is 3, and PRM is superior to PRB when the scale of the problem is large.

A NEW EFFICIENT ID-BASED PROXY BLIND SIGNATURE SCHEME

In a proxy blind signature scheme,the proxy signer is allowed to generate a blind signature on behalf of the original signer. The proxy blind signature scheme is useful in several applications such as e-voting,e-payment,etc. Recently,Zheng,et al. presented an IDentity(ID) -based proxy blind sig-nature. In this paper,a new efficient ID-based proxy blind signature scheme from bilinear pairings is proposed,which can satisfy the security properties of both the proxy signatures and the blind signature schemes. Analysis of the scheme efficiency shows that the new scheme is more efficient than Zheng,et al.'s scheme. The proposed scheme is more practical in the real world.

Linguistic Truth Values Lattice Implication Algebras

In order to study uncertainty reasoning and automatic reasoning with linguistic terms, in this paper, the set of basic linguistic truth values and the set of modifiers are defined, according to common sense; partially orderings are defined on them. Based on it, a lattice implication algebra model L18 of linguistic terms is built; furthermore, its some basic properties are discussed.

Analytical Results of Eigenstates and Eigenenergies for Three Kinds of Models Describing N-mode Multiphoton Process

We obtain. the exact analytical results of all the eigenvalues and eigenstates for three kinds of models describing N-mode multiphoton process without using the assumption of the Bethe ansatz. The exact analytical results of all the eigenstates and eigenvalues are in terms of a parameter lambda for three kinds of models describing N-mode multiphoton process. The parameter is shown to be determined by the roots of a polynomial and is solvable analytically or numerically. Moreover, these three kinds of models can be processed with the same procedure.

An Algebraic Approach to the Schwarz Alternating Methods

In this paper, the choice of the optimal parameters for a relaxation additive Schwarz alternating method in two subregions case is obtained by an algebraic method, which shows that the arithmetic average is the best. A counterexample illustrates that the same result is not true for many subregions case. In the last, this technique is applied to demonstrate some well known results ,, simply and intuitively.

FINDING THE TOPOLOGY OF IMPLICITLY DEFINED TWO ALGEBRAIC PLANE CURVES

An algorithm is given for computing in a very efficient way the topology of two real algebraic plane curves defined implicitly.The authors preform a symbolic pre-processing that allows us later to execute all numerical computations in an accurate way.