同伦方法求解非凸区域Brouwer不动点问题

本文构造了一个新的求解非凸区域上不动点问题的内点同伦算法,并在弱法锥(见定义2．1(2))和适当的条件下,证明了算法的全局收敛性．本文所给的条件比外法锥条件更加一般．     

A Homotopy Algorithm for Solving the Inverse Eigenvalue Problem for Complex Symmetric Matrices

A homotopy algorithm for solving the inverse eigenvalue problem for complex symmetric matrices is suggested. Some numerical examples are presented.     

同伦摄动法在求解四阶边值问题中的应用

将同伦摄动法用于求解常微分方程四阶边值问题.通过将常微分方程边值问题转化为积分方程组,应用同伦摄动法求得近似解.给出同伦摄动法在两个具体的实例中的应用,并将近似解与精确解进行了比较,验证了同伦摄动法对求解线性、非线性常微分方程边值问题是一种非常有效的方法.     

Hermite流形上Coupled Vortex方程的Dirichlet问题

本文研究Coupled Vortex方程的Dirichlet问题,通过热流方法来讨论该方程Dirichlet问题的解的存在唯一性．     

A Randomized Algorithm for a Sequence 2-Clustering Problem

Computational Mathematics and Mathematical Physics - We consider a strongly NP-hard problem of partitioning a finite Euclidean sequence into two clusters of given cardinalities minimizing the sum...     

四元数体上Hermite矩阵的最小化问题

该文建立了四元数矩阵对的标准相关分解(CCD-Q). 借助CCD-Q, GSVD-Q 和有限维内积空间中的投影定理, 该文得到了基于四元数矩阵方程$AXB=C$的Hermite矩阵最小化问题解的表达式.     

A Sufficient Criterion for Homotopy Cartesianess

Suppose given a commutative quadrangle in a Verdier triangulated category such that there exists an induced isomorphism on the horizontally taken cones. Suppose that the endomorphism ring of the initial or the terminal corner object of this quadrangle satisfies a finiteness condition. Then this quadrangle is homotopy cartesian.     

A Springer Theorem for Hermitian forms

Throughout this paper, we let (D,σ) be a central F -division algebra with involution σ such that F^σ={d ∈ F|σ(d)=d} is a Henselian valued field. By [11], the valuation on F^σ extends uniquely to a valuation on D. We denote this valuation by v. Moreover, we assume that the characteristic of the residue field, , is not 2. If the valuation on F is discrete, then any quadratic form q can be written as q= q₁⊥πq₂, where π is a uniformizer and q_i are unit forms. Springer's Theorem states that q is isotropic if and only if at least one of the residue forms and is isotropic. In this paper we generalize this result to ɛ -Hermitian forms. In Section 4, we use the connection between involutions on algebras and ɛ-Hermitian forms to prove an analog of the Springer Theorem for involutions. This paper was part of the author's doctoral dissertation at New Mexico State University. The author wishes to thank his advisor Pat Morandi for his tireless help.     

A real algorithm for the Hermitian eigenvalue decomposition

Modifying complex plane rotations, we derive a new Jacobi-type algorithm for the Hermitian eigendecomposition, which uses only real arithmetic. When the fast-scaled rotations are incorporated, the new algorithm brings a substantial reduction in computational costs. The new method has the same convergence properties and parallelism as the symmetric Jacobi algorithm. Computational test results show that it produces accurate eigenvalues and eigenvectors and achieves great reduction in computational time.The work of this author was supported in part by the National Science Foundation grant CCR-8813493 and by the University of Minnesota Army High Performance Computing Research Center contract DAAL 03-89-C-0038.The work of this author was supported in part by the University of Minnesota Army High Performance Computing Research Center contract DAAL 03-89-C-0038.     

用同伦方法求Picard边值问题的解

This paper deals with the problem of finding solutions to the Picard boundary problem. In our approach, by means of the homotopy method, the equation considered is linked to a simpler equation by introducing a parameter. We first find the solutions of the simpler equation, and give a priori estimates of" the equa tion we considered, and then one can obtain the solutions of Picard boundary problem by following the path of solutions of Cauchy problem.     

A Cauchy kernel for the Hermitian submonogenic system

Hermitian monogenic functions are the null solutions of two complex Dirac type operators. The system of these complex Dirac operators is overdetermined and may be reduced to constraints for the Cauchy datum together with what we called the Hermitian submonogenic system (see [8], [9]). This last system is no longer overdetermined and it has properties that are similar to those of the standard Dirac operator in Euclidean space, such as a Cauchy–Kowalevski extension theorem and Vekua type solutions. In this paper, we investigate plane wave solutions of the Hermitian submonogenic system, leading to the construction of a Cauchy kernel. We also establish a Stokes type formula that, when applied to the Cauchy kernel provides an integral representation formula for Hermitian submonogenic functions.     

On The Randomized Schmitter Problem

Methodology and Computing in Applied Probability - We revisit the classical Schmitter problem in ruin theory and consider it for randomly chosen initial surplus level U. We show that the...     

A New Homotopy Method for Nonlinear Complementarity Problems

In this paper, we present a new homotopy method for the nonlinear complementarity problems. Without the regularity or non-singulary assumptions for▽F(x), we prove that our homotopy equations have a bounded solution curve. The numerical tests confirm the efficiency of our proposed method.     

Solution of the Problem of Optimal Diagonal Scaling for Quasireal Hermitian Positive-Definite 3×3 Matrices

The paper completely solves the problem of optimal diagonal scaling for quasireal Hermitian positive-definite matrices of order 3. In particular, in the most interesting irreducible case, it is demonstrated that for any matrix C from the class considered there is a uniquely determined optimally scaled matrix D ₀ ^* CD₀ of one of the four canonical types. Formulas for the entries of the diagonal matrix D₀ are presented, as well as formulas for the eigenvalues and eigenvectors of D ₀ ^* CD₀ and for the optimal condition number of C, which is equal to k(D ₀ ^* CD₀). The optimality of the Jacobi scaling is analyzed. Bibliography: 10 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 309, 2004, pp. 84–126.     

Randomized Algorithms over Finite Fields for the Exact Parity Base Problem

We present three randomized pseudo-polynomial algorithms for the problem of finding a base of specified value in a weighted represented matroid subject to parity conditions. These algorithms, the first two being an improved version of those presented by P. M. Camerini et al. (1992, J. Algorithms13, 258–273) use fast arithmetic working over a finite field chosen at random among a set of appropriate fields. We show that the choice of a best algorithm among those presented depends on a conjecture related to the best value of the so-called Linnik constant concerning the distribution of prime numbers in arithmetic progressions. This conjecture, which we call the C-conjecture, is a strengthened version of a conjecture formulated in 1934 by S. Chowla. If the C-conjecture is true, the choice of a best algorithm is simple, since the last algorithm exhibits the best performance, either when the performance is measured in arithmetic operations, or when it is measured in bit operations and mild assumptions hold. If the C-conjecture is false we are still able to identify a best algorithm, but in this case the choice is between the first two algorithms and depends on the asymptotic growth of m with respect to those of U and n, where 2n, 2m, U are the rank, the number of elements, and the maximum weight assigned to the elements of the matroid, respectively.