Construction of Runge–Kutta methods of Crouch–Grossman type of high order

An approach is described to the numerical solution of order conditions for Runge–Kutta methods whose solutions evolve on a given manifold. This approach is based on least squares minimization using the Levenberg–Marquardt algorithm. Methods of order four and five are constructed and numerical experiments are presented which confirm that the derived methods have the expected order of accuracy.     

SUBSPACE SEARCH METHOD FOR A CLASS OF LEAST SQUARES PROBLEM

1. IntroductionNow the least squares problem is considered as follows:1Mid r(x,y) ~ SllAx By ~ bll' s.t. x 2 0 (1.1)where A E Rm",, B E R"q, and b E Re are given constant matrices and vectors,respectively.These problems arise in many areas of applications, such as scientific and engineering computing, physics, statistics, flited curve, economic, mathematical programming,social science, and as a component part of some large computation problem, as anexample, a nonlinear least squares pr…     

Global,local and unique decompositions in OnPLS for multiblock data analysis

OnPLS is an extension of O2PLS that decomposes a set of matrices, in either multiblock or path model analysis, such that each matrix consists of two parts: a globally joint part containing variation shared with all other connected matrices, and a part that contains locally joint and unique variation, i.e. variation that is shared with some, but not all, other connected matrices or that is unique in a single matrix.     

A locally conservative,discontinuous least‐squares finite element method for the Stokes equations

Conventional least‐squares finite element methods (LSFEMs) for incompressible flows conserve mass only approximately. For some problems, mass loss levels are large and result in unphysical solutions. In this paper we formulate a new, locally conservative LSFEM for the Stokes equations wherein a discrete velocity field is computed that is point‐wise divergence free on each element. The central idea is to allow discontinuous velocity approximations and then to define the velocity field on each element using a local stream‐function. The effect of the new LSFEM approach on improved local and global mass conservation is compared with a conventional LSFEM for the Stokes equations employing standard C⁰ Lagrangian elements. Copyright © 2011 John Wiley & Sons, Ltd.     

Capability of Urine Analysis for the Disease Blastomycosis Using Infrared Spectroscopy with Eigenvector Signal to Noise Assessment

ABSTRACT

Blastomyces dermatitidis is the etiological agent of the relatively common disease blastomycosis found in certain regions of the United States. In order to discern the presence of blastomycosis, microorganisms present in biofluids of infected individuals must be incubated and cultured and then identified by microscopic observation. This procedure is time consuming due to difficult incubation conditions and necessitates special safeguards. An enzyme-linked immunosorbent assay (ELISA) was developed in an attempt to quicken diagnosis. The immunological assay, however, also requires incubations as well as special reagents. This paper explores the potential of using infrared spectroscopy for determination of blastomycosis in urine samples from infected dogs. The regression methods of principal component regression (PCR) and partial least squares (PLS) are used to develop models. Recently introduced regression diagnostics in conjunction with new diagnostic tools described in this paper are used to determine final models. One of the new tools allows for an estimate of the signal (information) to noise ratio, i.e., reliability, for each eigenvector's contribution to the model. Based on diagnostic information, it is concluded that PCR and PLS are generating the same models.     

A geometric view of Krylov subspace methods on singular systems

We give a geometric framework for analysing iterative methods on singular linear systems A x = b and apply them to Krylov subspace methods. The idea is to decompose the method into the ?(A) component and its orthogonal complement ?(A)^?, where ?(A) is the range of A. We apply the framework to GMRES, GMRES(k) and GCR(k), and derive conditions for convergence without breakdown for inconsistent and consistent singular systems. The approach also gives a geometric interpretation and different proofs of the conditions obtained by Brown and Walker for GMRES. We also give examples arising in the finite difference discretization of two‐point boundary value problems of an ordinary differential equation. Copyright © 2010 John Wiley & Sons, Ltd.     

Practical approaches to principal component analysis for simultaneously dealing with missing and censored elements in chemical data

Multivariate chemical data often contain elements that are missing completely at random and the so-called left-censored elements whose values are only known to be below a definite threshold value (reporting limit). In the last several years, attention has been paid to developing methods for dealing with data containing missing elements and those that can handle data with missing elements and outliers. However, processing data with both missing and left-censored elements is still an ongoing problem.     

基于NLMS自适应滤波的近红外光谱去噪处理方法研究

为了去除直接采集的近红外(NIR)光谱中含有的噪声,将归一化最小均方(NLMS)自适应滤波方法引入到NIR光谱去噪领域中。以51份土壤样品的NIR光谱为研究对象,探讨NLMS自适应滤波方法在NIR光谱预处理中的应用,并将处理后的结果与土壤中有机质的含量相关联,建立模型。结果表明,通过NLMS自适应滤波去噪后的光谱,预测集的相关系数r由处理前的0.8284提高至0.9654,预测均方根误差(RMSEP)由处理前的0.3385降至0.1606。由此可见,NLMS自适应滤波对NIR光谱的去噪有显著效果,可以有效地提高光谱的分析精度和模型的稳健性,为NIR光谱的预处理提供了一种新方法。