Browsing Computational and Applied Mathematics by Title
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Taguchi and Robust Optimization
(199610)This report is intended to facilitate dialogue between engineers and optimizers about the efficiency of Taguchi methods for robust design, especially in the context of design by computer simulation. Three approaches to ... 
The Acoustic Radiation Solution
(200810)The wellknown radiation solution of the acoustic wave equation may also be viewed as the pressure field in the solution of the firstorder system of linear acoustics, in two different ways. The first version casts in the ... 
The Arnoldi Eigenvalue Iteration with Exact Shifts Can Fail
(200609)The restarted Arnoldi algorithm, implemented in the ARPACK software library and MATLAB's eigs command, is among the most common means of computing select eigenvalues and eigenvectors of a large, sparse matrix. To assist ... 
The Bayesian Statistical Approach to the Phase Problem in Protein Xray Crystallography
(199904)We review a Bayesian statistical approach to the phase problem in protein Xray crystallography. We discuss the mathematical foundations and the computational issues. The introduction to the theory and the algorithms does ... 
The Behavior of NewtonType Methods on Two Equivalent Systems from Linear Programming
(199802)Newtontype methods are fundamental techniques for solving optimization problems. However, it is often not fully appreciated that these methods can produce significantly different behavior when applied to two equivalent ... 
The Combined Schubert/Secant/Finite Difference Algorithm for Solving Sparse Nonlinear Systems of Equations
(198605)This paper presents an algorithm, the combined Schubert/secant/finite difference algorithm, for solving sparse nonlinear systems of equations. This algorithm is based on dividing the columns of the Jacobian into two parts, ... 
The Computation of Elementary Unitary Matrices
(199402)The construction of elementary unitary matrices that transform a complex vector to a real multiple of e1, the first column of the identity matrix, is studied. We survey the two well known forms and present what appears to ... 
The DikinKarmarkar Principle for Steepest Descent
(199209)Steepest feasible descent methods for inequality constrained optimization problems have commonly been plagued by short steps. The consequence of taking short steps is slow convergence to nonstationary points (zigzagging). ... 
The Effect of Caustics in Acoustic Inverse Scattering Experiments
(198905)Most inversion techniques described in the literature rely on the validity of ray tracing, which breaks down in the presence of caustics. The linearized acoustic inverse problem with constant reference velocity is analyzed ... 
The Effect of the Definition of Fractional Flow Upon Grid Effects in a Numerical Model of Thermal Processes
(198303)In previous research regarding the numerical simulation of a single phase miscible displacement, a numerical procedure which does not exhibit serious grid effects and is highly compatible with nine point finite difference ... 
The Effect of the Separation of Variables on the Molecular Replacement Method
(200006)Traditional approaches for solving the molecular replacement problem separate a sixdimensional optimization problem into two threedimensional ones in order to reduce the computational cost. There are, however, serious ... 
The Existence of Weak Solutions to Single Porosity and Simple DualPorosity Models of TwoPhase Incompressible Flow
(199202)It is shown that there exists a weak solution to a degenerate and singular ellipticparabolic partial integrodifferential system of equations. These equations model twophase incompressible flow of immiscible fluids in ... 
The Formulation and Solution of Multidimensional Scaling Problems
(199311)Numerous experiments in a variety of applied disciplines involve measuring distances between pairs of objects. The statistical problem posed by such experiments is that of fitting the observed data with a model defined to ... 
The Inverse Problem of Neuron Identification
(200005)Depending on the state of neuron membrane, the inverse problem of neuron identification is divided into two categories: the passive neuron identification and the active neuron identification. In the first category, we ... 
The Lack of Positive Definiteness in the Hessian in Constrained Optimization
(198306)The use of the DFP or the BFGS secant updates requires the Hessian at the solution to be positive definite. The second order sufficiency conditions insure the positive definiteness only in a subspace of R^n. Conditions are ... 
The Lagrangian and Other Primal Cutting Planes for Linear Integer Programming Problems
(199003)Cutting plane methods and Lagrangian relaxation have both proven to be powerful methods in the solution of integer programs. The purpose of this paper is to interpret Lagrangian relaxation as a cutting plane technique and ... 
The Lagrangian as a Primal Cutting Plane Method for Linear Integer Programming Problems
(198812)Lagrangian relaxation and more recently cutting plane techniques have both proven to be powerful methods in the solution of integer problems. This paper explores the relationship between these techniques by interpreting ... 
The Local Convergence of Sequential Quadratic Programming Methods
(198703)Sequential quadratic programming methods for solving constrained nonlinear optimization problems (P) generate iterates xk, x{k+1}: = Phi</(xk), by means of a certain iteration function Phi(xk), which has any KuhnTucker ...