Linear low-rank approximation and nonlinear dimensionality reduction

We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of column-partitioned matrices and sparse low-rank approximation; for the nonlinear case we investigate methods for nonlinear dimensionality reduction and manifold learning. The problems we address have attracted great deal of interest in data mining and machine learning.     

连铸结晶器内部流场及熔渣卷入的数值模拟

针对连铸结晶器内部流场及熔渣卷入过程 ,提出了两方程k -ε湍流模型和充填法数值计算模型 ,并采用硅油 /水模拟体系代替熔渣 /钢液体系 ,进行了模拟试验和数值计算。对充气造成的浸入式水口水流脉动的影响进行分析。计算结果与试验结果符合良好 ,表明本文所采用的数值模拟方法是适用的     

异质结太阳电池硅衬底绒面陷光结构的优化

硅异质结(SHJ)太阳电池作为备受关注的新型高效太阳电池,是在单晶硅表面沉积非晶硅薄膜制备而成的。将绒面结构的单晶硅衬底应用于异质结太阳电池,可以减少光的反射,增强光吸收的效率,从而提高太阳电池短路电流密度。利用湿法化学腐蚀对单晶硅衬底表面进行制绒,通过优化影响绒面形貌的几个关键参数,包括异丙醇浓度、时间、衬底类型和硅酸钠的含量,最终通过在n型单晶硅衬底上制绒,使波长为1011 nm处最低反射率从制绒前的34.7%降低到了9.14%,将制绒衬底应用到异质结太阳电池上,短路电流由32.06 m A/cm-2提升到36.16 m A/cm-2,有效地改善了SHJ太阳电池的性能。     

Successive projection method for solving the unbalanced Procrustes problem

We present a successive projection method for solving the unbalanced Procrustes problem: given matrix A∈Rn×n and B∈Rn×k, n>k, minimize the residual‖AQ-B‖F with the orthonormal constraint QTQ = Ik on the variant Q∈Rn×k. The presented algorithm consists of solving k least squares problems with quadratic constraints and an expanded balance problem at each sweep. We give a detailed convergence analysis. Numerical experiments reported in this paper show that our new algorithm is superior to other existing methods.     

A sorted partial jacobi method and its convergence analysis

Jacobi methods for computing the eigendecomposition of a class of so-called low-rank-plus-shift symmetric matrices are investigated. An order-of-magnitude reduction in the computational complexity can be achieved for this special class of matrices by terminating the Jacobi sweep early in a cyclic ordering. It is proved that these partial sweeps combined with sorting the diagonals still deliver quadratic convergence. It is also shown that useful results can still be obtained even if the low-rank-plus-shift structure only holds approximately.     

Modifying the generalized singular value decomposition with application with application in direction-of-arrival finding

We consider updating and downdating problems for the generalized singular value decomposition (GSVD) of matrix pairs when new rows are added to one of the matrices or old rows are deleted. Two classes of algorithms are developed, one based on the CS decomposition formulation of the GSVD and the other based on the generalized eigenvalue decomposition formulation. In both cases we show that the updating and downdating problems can be reduced to a rank-one SVD updating problem. We also provide perturbation analysis for the cases when the added or deleted rows are subject to errors. Numerical experiments on direction-of-arrival (DOA) finding with colored noises are carried out to demonstrate the tracking ability of the algorithms. The work of the first author was supported in part by NSF grants CCR-9308399 and CCR-9619452. The work of the second author was supported in part by China State Major Key Project for Basic Researches.     

Design of dispersive multilayer with particle swarm optimization method

<正>We present a new and efficient method for the design of dispersive multilayer by employing a particle swarm optimization(PSO) technique.Its mathematical background is given and an adaptive PSO is realized with computer code.Two practical designing tasks are solved with this method,and the obtained results are competitive compared with other published structures.The adaptive PSO method demonstrates its merits of fast convergence and powerful global search ability,and could be used as a valuable tool for the optical thin film design.     

Alloying n‐Butylamine into CsPbBr3 To Give a Two‐Dimensional Bilayered Perovskite Ferroelectric Material

Cesium‐lead halide perovskites (e.g. CsPbBr₃) have gained attention because of their rich physical properties, but their bulk ferroelectricity remains unexplored. Herein, by alloying flexible organic cations into the cubic CsPbBr₃, we design the first cesium‐based two‐dimensional (2D) perovskite ferroelectric material with both inorganic alkali metal and organic cations, (C₄H₉NH₃)₂CsPb₂Br₇ ( 1 ). Strikingly, 1 shows a high Curie temperature (T_c=412 K) above that of BaTiO₃ (ca. 393 K) and notable spontaneous polarization (ca. 4.2 μC cm^?2), triggered by not only the ordering of organic cations but also atomic displacement of inorganic Cs⁺ ions. To our knowledge, such a 2D bilayered Cs⁺‐based metal–halide perovskite ferroelectric material with inorganic and organic cations is unprecedented. 1 also shows photoelectric semiconducting behavior with large “on/off” ratios of photoconductivity (>10³).     

Measurement of absolute phase Shift on reflection of thin films using white-light spectral interferometry

A novel method to measure the absolute phase shift on reflection of thin film is presented utilizing a white-light interferometer in spectral domain. By applying Fourier transformation to the recorded spectral interference signal, we retrieve the spectral phase function Ф, which is induced by three parts： the path length difference in air L, the effective thickness of slightly dispersive cube beam splitter Teff and the nonlinear phase function due to multi-reflection of the thin film structure. We utilize the fact that the overall optical path difference （OPD） is linearly dependent on the refractive index of the beam splitter to determine both L and Teff. The spectral phase shift on reflection of thin film structure can be obtained by subtracting these two parts from Ф. We show theoretically and experimentally that our new method can provide a simple and fast solution in calculating the absolute spectral phase function of optical thin films, while still maintaining high accuracy.     

Convergence analysis of generalized nonlinear inexact Uzawa algorithm for stabilized saddle point problems

This paper deals with a modified nonlinear inexact Uzawa (MNIU) method for solving the stabilized saddle point problem. The modified Uzawa method is an inexact inner-outer iteration with a variable relaxation parameter and has been discussed in the literature for uniform inner accuracy. This paper focuses on the general case when the accuracy of inner iteration can be variable and the convergence of MNIU with variable inner accuracy, based on a simple energy norm. Sufficient conditions for the convergence of MNIU are proposed. The convergence analysis not only greatly improves the existing convergence results for uniform inner accuracy in the literature, but also extends the convergence to the variable inner accuracy that has not been touched in literature. Numerical experiments are given to show the efficiency of the MNIU algorithm.