Globally convergent algorithm for solving nonlinear equations

A general iterative method is proposed for finding the maximal rootx _max of a one-variable equation in a given interval. The method generates a monotone-decreasing sequence of points converging tox _max or demonstrates the nonexistence of a real root. It is globally convergent. A concrete realization of the general algorithm is also given and is shown to be locally quadratically convergent. Computational experience obtained for eight test problems indicates that the new method is comparable to known methods claiming global convergence.     

紧拓扑半群上概率测度卷积序列的极限性质

本文讨论紧拓扑半群上概率测度卷积序列的若干重要极限性质．在第１节中，我们讨论测度集的代数结构与其支撑集代数结构的关系．第２节的定理１，通过支撑集的代数结构给出组合收敛测度序列的一个极限定理．在定理２中我们讨论独立同分布时的情形，建立了一类紧半群上的Ｋａｗａｄａ－Ｉｔ型结果．这些定理推广了紧群、紧交换半群、紧Ｌ－Ｘ半群上一些相应的结论．     

Spectral Convergence for Degenerating Sequences of Three Dimensional Hyperbolic Manifolds

For degenerating sequences of three dimensional hyperbolic manifolds of finite volume, we prove convergence of their eigenfunctions, heat kernel and spectral measure.

     

THE SIMPLE BLOCK ITERATIVE ALGORITHM OF AN EXTENDED ENTROPY MODEL AND ITS CONVERGENCE

1.ExtendedEntropyModelEntropymodelsarewidelyusedasaforecastingtechniqueinregionalplanning,see11]and[7].Theydescribeinacertainwaythemostprobablespatialinteractionandcanbeusedtoestimateorigin-destinationtripmatrices.Butthemodelsaretoosimple,soitisdifficulttomeetpracticalrequirements.HallefjordandJo..stenl2]putforwardthegeneralizationofthestandardentropymodels.Onthebasisofthisandaccordingtothedemandofthepredictionofthetripamountfortransportationplanning,wearriveatthefollowing:wherep,μandnarepo…     

A CLASS OF FACTORIZATION UPDATE ALGORITHM FOR SOLVING SYSTEMS OF SPARSE NONLINEAR EQUATIONS

ＡＣＬＡＳＳＯＦＦＡＣＴＯＲＩＺＡＴＩＯＮＵＰＤＡＴＥＡＬＧＯＲＩＴＨＭＦＯＲＳＯＬＶＩＮＧＳＹＳＴＥＭＳＯＦＳＰＡＲＳＥＮＯＮＬＩＮＥＡＲＥＱＵＡＴＩＯＮＳＢＡＩＺＨＯＮＧＺＨＩ（ＩｎｓｔｉｔｕｔｅｏｆＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔｉｃ...     

纯正半群上的同余扩张(一)

刻划半群上的同余及其扩张是半群的代数理论中的一个非常重要的课题．本文讨论了带上的同余的正规性和不变性以及在其Ｈａｌｌ半群上的扩张，从同余扩张的角度刻划了带上的同余的性质，给出了扩张的极大、极小同余的描述．     

The Hilbert Kernel Regression Estimate

Let (X, Y) be an ^d× -valued regression pair, whereXhas a density andYis bounded. Ifni.i.d. samples are drawn from this distribution, the Nadaraya–Watson kernel regression estimate in ^dwith Hilbert kernelK(x)=1/x^dis shown to converge weakly for all such regression pairs. We also show that strong convergence cannot be obtained. This is particularly interesting as this regression estimate does not have a smoothing parameter.     

GMRES and the minimal polynomial

We present a qualitative model for the convergence behaviour of the Generalised Minimal Residual (GMRES) method for solving nonsingular systems of linear equationsAx =b in finite and infinite dimensional spaces. One application of our methods is the solution of discretised infinite dimensional problems, such as integral equations, where the constants in the asymptotic bounds are independent of the mesh size.Our model provides simple, general bounds that explain the convergence of GMRES as follows: If the eigenvalues ofA consist of a single cluster plus outliers then the convergence factor is bounded by the cluster radius, while the asymptotic error constant reflects the non-normality ofA and the distance of the outliers from the cluster. If the eigenvalues ofA consist of several close clusters, then GMRES treats the clusters as a single big cluster, and the convergence factor is the radius of this big cluster. We exhibit matrices for which these bounds are tight.Our bounds also lead to a simpler proof of existing r-superlinear convergence results in Hilbert space.This research was partially supported by National Science Foundation grants DMS-9122745, DMS-9423705, CCR-9102853, CCR-9400921, DMS-9321938, DMS-9020915, and DMS-9403224.     

非线性ABS型算法的一个统一收敛定理

本文讨论非线性方程组的算法的局部收敛性，给出了一个统一的收敛定理．该定理相当一般，不仅包含ＡＢＳ型方程，而且对目前常用的许多方法也都适用．     

A Novel Fiber Taper for Efficient Optical Interconnection

１ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｅｒｃｏｎｎｅｃｔｉｏｎｓｏｆｏｐｔｉｃａｌｗａｖｅｇｕｉｄｅｃｏｍｐｏｎｅｎｔｓｗｉｔｈｄｉｆｅｒｅｎｔｍｏｄａｌｓｐｏｔｓｉｚｅｓ，ｐａｒｔｉｃｕｌａｒｌｙｆｏｒｔｈｅｃｏｎｎｅｃｔｉｏｎｏｆ（１）ｌａｓｅｒｓｏｕ...