r-循环线性系统求解的快速算法

本文给出r-循环线性系统求解的一种快速算法.当r-循环矩阵非奇异时,该快速算法求出该线性系统的唯一解;当r-循环矩阵奇异时,该快速算法求出该线性系统的通解.     

Transputer上Cholesky分解的并行实现

§1.引言 对称正定矩阵A的Cholesky分解在求解线性系统Ax-b中非常重要,如果R是上三角矩阵,使得A=R~TR,则求解上述方程组可以通过向前及向后迭代来完成。然而求解一个线性系统,主要是计算系数矩阵的分解。这里主要是介绍如何有效地并行求矩阵R。在串行机上,已经有了很好的实现方法,如[1]至于如何在并行机上实现,是本文的目的。 众所周知,在并行机上求解大规模问题是今后科学与工程计算的必然发展方向。然     

求解增广线性系统的局部多分裂迭代法

为了在高性能计算机上求解增广线性系统,基于并行多分裂的两种技巧,本文提出一种局部多分裂迭代格式,给出当增广线性系统的矩阵为M-矩阵和H-矩阵时新方法的收敛性理论.并讨论预条件矩阵的特征值情形.     

求解M-张量方程的两种新型算法

多重线性系统在当今的工程计算和数据挖掘等领域有很多实际应用,许多问题可以转化为多重线性系统求解问题.在本文中,我们首先提出了一种新的迭代算法来求解系数张量为M-张量的多重线性系统,在此基础上又提出了一种新的改进算法,并对两种算法的收敛性进行了分析.数值算例的结果表明,本文提出的两种算法是有效的并且改进算法的迭代时间更少.     

广义线性系统Ex=Ax解的存在唯一性

研究了广义线性系统Ex=AX的初值问题解的存在唯一性的充要条件和求解公式．     

关于TLS问题

1.引 言考虑观测线性系统AX=B,（1.1a）其中A∈Cm×n,B∈Cm×d（本文通篇假设m≥n d）,分别是精确但不可观测的A0∈Cm×n,B0∈Cm×d的近似,即精确线性系统是A0X=B0.（1.1b）Golub和Van Loan于1980年提出的总体最小二乘问题（以下简称TLS问题）就是求解线性系统AX=B（1.2）     

广义H-矩阵的乘积的性质

1 引言 广义M-矩阵和广义H-矩阵的理论在许多实际问题的研究中有着非常重要的作用,如欧拉方程数值求解中出现的线性系统的块迭代法的收敛性问题,以及动力系统的研究等.     

一类线性系统的数值控制设计

主要讨论了具有不稳定切换子模型的切换线性系统的稳定性问题.首先考虑了通过设计切换律来达到切换线性系统的稳定性问题.然后研究了切换线性控制系统可镇定性问题,通过设计控制律和切换律得到系统可镇定的判据.     

奇异模糊线性系统的扰动分析

当模糊线性系统的系数矩阵奇异时, 分析了模糊线性系统的右端向量和系数矩阵的扰动对模糊线性系统解的计算造成的影响,用矩阵的谱范数给出了相对误差的界.     

GSOR方法最优迭代参数的简化推导

对于增广线性系统,Bai等研究了广义SOR方法（Bai Z Z,Parlett B,Wang Z Q.On generaliged successive overrelaxation methods for augmented linear systems.Numerische Mathematik,2005,102（1）：1-38）,并得到其最优迭代参数.给出了另外一种推导最优迭代参数的简化方法,这种方法对于求解其他参数加速定常迭代方法的最优迭代参数非常有意义.     

Two-time Green’s functions in superconductivity theory

Based on the method of the equations of motion for two-time Green’s functions, we derive superconductivity equations for different types of interactions related to the scattering of electrons on phonons and spin fluctuations or caused by strong Coulomb correlations in the Hubbard model. We derive an exact Dyson equation for the matrix Green’s function with the self-energy operator in the form of the multiparticle Green’s function. Calculating the self-energy operator in the approximation of noncrossing diagrams leads to a closed system of equations corresponding to the Migdal-Eliashberg strong-coupling theory. We propose a theory of high-temperature superconductivity due to kinematic interaction in the Hubbard model. We show that two pairing channels occur in systems with a strong Coulomb correlation: one due to the antiferromagnetic exchange in interband hopping and the other due to the coupling to spin and charge fluctuations in hopping within one Hubbard band. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 129–146, January, 2008.     

On high-temperature superconductivity

We consider electron-phonon interaction models for the case of strong coupling as well as the well-known Hubbard model. We write out the asymptotics as the number of electrons tends to infinity; this allows us to determine the temperature of the superconducting-to-normal state phase transition and the jump in the heat capacity. Translated fromMatematicheskie Zametki, Vol. 66, No. 5, pp. 706–722, November, 1999.     

Asymmetric Hubbard model in the generating functional method: Spectral functions in the Falicov-Kimball limit

In the framework of the dynamical mean field theory, we investigate the densities of states of the fermionic and bosonic branches of the spectrum of the asymmetric Hubbard model, which is used to describe a strongly correlated two-sort (A, B) system of fermions (electrons). To solve the effective one-site problem, we develop an approximate analytic approach based on the Kadanoff-Baym generating functional method. This technique allows constructing the irreducible part (the mass operator) of the particle Green’s function in the form of a formal expansion in powers of the coherent potential. In the first order, the scheme reproduces the so-called generalized approximation Hubbard-III. To improve it, we develop a self-consistent method for calculating both the fermionic and bosonic Green’s functions. As U → ∞ in the Falicov-Kimball limit for the asymmetric Hubbard model, when the particles of sort B become localized, we find the spectral densities ρ_B and ρ_AB of states of both branches and consider the changes of their forms depending on temperature and particle concentrations. Comparing with the exact thermodynamic dependences μ_B(n_B), we establish the applicability limits of the self-consistent generalized approximation Hubbard-III. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 164–182, January, 2008.     

Inverse limits of postcritically finite polynomials

We examine inverse limits of postcritically finite polynomials restricted to their Julia sets. We define the “trunk” of a Julia set, a forward-invariant set related to the Hubbard tree, and use it to show that the inverse limit always contains at least one indecomposable subcontinuum. We characterize when the inverse limit is indecomposable and also examine how the trunk behaves in the inverse limit.     

A discrete “three-particle” Schrödinger operator in the Hubbard model

In the space L ₂(T ^ν ×T ^ν ), where T ^ν is a ν-dimensional torus, we study the spectral properties of the “three-particle” discrete Schrödinger operator ? = H₀ + H₁ + H₂, where H₀ is the operator of multiplication by a function and H₁ and H₂ are partial integral operators. We prove several theorems concerning the essential spectrum of ?. We study the discrete and essential spectra of the Hamiltonians H^t and h arising in the Hubbard model on the three-dimensional lattice.     

Exact solutions of the high dimensional hard-core Fermi-Hubbard model

A simple algebraic approach to exact solutions of the hard-core Fermi-Hubbard model is proposed. Excitation energies and the corresponding wavefunctions of the hard-core Fermi-Hubbard model with nearest neighbor hopping cases in high dimension are obtained by using this method, which manifests that the model is exactly solvable in any dimension.     

Supergroup approach to the Hubbard model

Based on the revealed hidden supergroup structure, we develop a new approach to the Hubbard model. We reveal a relation of even Hubbard operators to the spinor representation of the generators of the rotation group of four-dimensional spaces. We propose a procedure for constructing a matrix representation of translation generators, yielding a curved space on which dynamic superfields are defined. We construct a new deformed nonlinear superalgebra for the regime of spinless Hubbard model fermions in the case of large on-site repulsion and evaluate the effective functional for spinless fermions     

Study of the Hubbard model at half filling

Under the conditions of a strong Coulomb repulsion between electrons at a lattice site, we now study the equations for the self-energy part of the electron Green’s function, which we previously obtained using the generating functional method. These equations have a form close to that corresponding to the self-consistent Born approximation in the weak-coupling theory. In these equations, we omit the dependence of the self-energy on the momentum, which corresponds to the infinite-dimensional space limit. We then numerically solve the integral equations, where all the variables depend only on the frequency, and obtain results consistent with the dynamical mean field theory. In particular, we show that as the Coulomb repulsion increases, the three-peak structure of the quasiparticle spectrum changes into a two-peak structure and the metal–insulator phase transition occurs. The proposed method can be used to study other models of the theory of strongly correlated systems. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 63–76, January, 2008.     

Dynamical Spin Susceptibility in the <Emphasis Type="Italic">t-J</Emphasis> Model: The Memory Function Method

Based on the method of the equations of motion for the relaxation function in terms of Hubbard operators, we evaluate the dynamical spin susceptibility for the t-J model in the paramagnetic phase. Using a Mori-type projection technique, we express the relaxation function in terms of the second-order memory function, which is evaluated in the approximation of coupled modes for hole excitations and spin fluctuations in the fourth order in the hopping parameter t and the exchange interaction J. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 2, pp. 240–255, November, 2005.     

The effective action and the spectrum of collective modes in the antiferromagnetic phase of the three-band repulsive hubbard model

The paper is concerned with the application of path integration (successive integration over “fast” and “slow” variables and the Hubbard-Stratonovich transformation) to the antiferromagnetic state in the three-band, two-dimensional repulsive Hubbard model. It is shown that, in the lowest approximation, the model under consideration is equivalent to the half-filled single-band Hubbard model. The effective action for the collective Bose-fields, the critical temperature of the phase transition, and the spectra of excitations are obtained. Bibliography: 24 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 245, 1997, pp. 216–230. Translated by C. L. Malyshev.