Steepest Descent, CG, and Iterative Regularization of Ill-Posed Problems

The state of the art iterative method for solving large linear systems is the conjugate gradient (CG) algorithm. Theoretical convergence analysis suggests that CG converges more rapidly than steepest descent. This paper argues that steepest descent may be an attractive alternative to CG when solving linear systems arising from the discretization of ill-posed problems. Specifically, it is shown that, for ill-posed problems, steepest descent has a more stable convergence behavior than CG, which may be explained by the fact that the filter factors for steepest descent behave much less erratically than those for CG. Moreover, it is shown that, with proper preconditioning, the convergence rate of steepest descent is competitive with that of CG.This revised version was published online in October 2005 with corrections to the Cover Date.     

Investigations in the amplitude of sounded piano tones

The relationship between final hammer velocity and maximum amplitude of radiated piano sound was investigated. Piano tones with varying hammer velocities were produced by a computer-monitored acoustic piano containing optical sensors and solenoids, and the sounded tones were recorded and digitized for analysis. Maximum amplitudes over the duration of the sounded tones were linearly proportional to piano hammer velocities for a range of frequencies and hammer velocities. Changes in room acoustics did not alter the linear relationship. Measurements of maximum amplitudes of individual tones and combined tones (dyads) also indicated a linear relationship between the sum of the maximum amplitudes of the individual tones and the maximum amplitude of the dyads. These findings indicate that the principle of superposition holds for peak amplitudes of sounded piano tones. Findings are discussed with regard to production and perception of musical dynamics.     

A novel detection scheme for vibration monitoring using optical techniques

An all-fibre interferometer which allows the measurement of the movement (speed and distance) of a vibrating body is presented. An electronic signal processing scheme is used and this is contrasted with the measurement of velocity through an optical processing technique, which is however, more complex and expensive to implement. The overall simplicity of the electronic technique, the low cost of components and the use of an all-fibre arrangement make this an attractive system to implement where the more limited information available is sufficient for monitoring purposes.     

广义风险过程中渐近方差的非参数估计

本文对广义风险过程中的渐近方差作了非参数估计,得出并证明了两个定理,为广义风险过程中破产概率的区间估计作了理论准备．     

3,3,6,6-四甲基-9-邻氯苯基-1,8-二氧代-3,4,5,6,7,9-六氧化氧杂蒽的合成和晶体结构

标题化合物C23H25对O3Cl是由邻氯苯甲醛与5，5-二甲基1，3-环己二酮在N，N-二甲基甲酸腹中反应而得。结构通过单晶X-射线衍射法确定，其晶体属于单科晶系，空间群=1632。晶体结构用直接法解出，使用全矩阵最小二乘法对原子参数进行修正，最后的偏离因子为R=0．054，Rw一0．063。在晶体结构中，吡喃环与苯环之间的两面角为92．43°。