Abstract: In the choice of an estimator for the spectrum of a stationary time series from a finite sample of the process, the problems of bias control and consistency, or "smoothing," are dominant. In this paper we present a new method based on a "local" eigenexpansion to estimate the spectrum in terms of the solution of an integral equation. Computationally this method is equivalent to using the weishted average of a series of direct-spectrum estimates based on orthogonal data windows (discrete prolate spheroidal sequences) to treat both the bias and smoothing problems. Some of the attractive features of this estimate are: there are no arbitrary windows; it is a small sample theory; it is consistent; it provides an analysis-of-variance test for line components; and it has high resolution. We also show relations of this estimate to maximum-likelihood estimates, show that the estimation capacity of the estimate is high, and show applications to coherence and polyspectrum estimates.

Abstract: The Waveform Relaxation (WR) method is an iterative method for analyzing nonlinear dynamical systems in the time domain. The method, at each iteration, decomposes the system into several dynamical subsystems each of which is analyzed for the entire given time interval. Sufficient conditions for convergence of the WR method are proposed and examples in MOS digital integrated circuits are given to show that these conditions are very mild in practice. Theoretical and computational studies show the method to be efficient and reliable.

Abstract: In this paper, we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems. Included among such methods are the Newton and several successive overrelaxation algorithms. For the most part, the study is concerned with the family of linear approximation methods. These are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems. Convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches. The paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria. Finally, several convergence results are obtained for some nonlinear approximation methods.

Abstract: A set of images is modeled as a stochastic process and Karhunen-Loeve expansion is applied to extract the feature images. Although the size of the correlation matrix for such a stochastic process is very large, we show the way to calculate the eigenvectors when the rank of the correlation matrix is not large. We also propose an iterative algorithm to calculate the eigenvectors which save computation time andc omputer storage requirements. This iterative algorithm gains its efficiency from the fact that only a significant set of eigenvectors are retained at any stage of iteration. Simulation results are also presented to verify these methods.

Abstract: Numerical methods for solving the integrodifferential, integral, and surface-integral forms of the neutron transport equation are reviewed. The solution methods are shown to evolve from only a few ...

Abstract: In this paper mathematician K.M. Brown's method is used to solve load-flow problems. The method is Particularly effective for solving of ill-conditioned non- linear algebraic equations. It is a variation of Newton's method incorporating Gaussian elimination in such a way that the most recent infonnation is always used at each step of the algorithm; similar to what is done in the Gauss-Seidel process. The iteration converges locally and the convergence is quadratic in nature. A general discussion of ill-conditioning of a system of algebraic equations is given, and it is also show by the fixed-point formulation that the proposed method falls in the general category of sucessive approximation methods. Digital computer solutions by the proposed method are given for cases for which the standard load-flow methods failed to converge, namely 11-, 13- and 43-bus ill-conditioned test systems. A comparison of this method with the standard load-flow methods is also presented for the well-conditioned AEP 30-, and 57-bus systems.

Abstract: Newton's method plays a central role in the development of numerical techniques for optimization In fact, most of the current practical methods for optimization can be viewed as variations on Newton's method It is therefore important to understand Newton's method as an algorithm in its own right and as a key introduction to the most recent ideas in this area One of the aims of this expository paper is to present and analyze two main approaches to Newton's method for unconstrained minimization: the line search approach and the trust region approach The other aim is to present some of the recent developments in the optimization field which are related to Newton's method In particular, we explore several variations on Newton's method which are appropriate for large scale problems, and we also show how quasi-Newton methods can be derived quite naturally from Newton's method

Abstract: The influence of the choice of the Lagrange multiplier on constrained linear inversions is explored, with reference made to applications in inferring the columnar aerosol size distributions from spectral aerosol optical depth measurements. A range of the Lagrange multiplier is examined to find all positive solutions for the solution vector, which represents modifying factors to the assumed form of the size distribution. An iterative method is devised to constrain the calculations to consideration of only positive quantities and a requirement that the regression fit to data be consistent with measurement errors. The determination of the variances and covariances is formulated and applied to existing data sets for optical depth. Variances in the solution are found to be large for particle radii when the information content of the data is small.

Abstract: In Part 1 of this study (Ref. 1), we have defined the implicit complementarity problem and investigated its existence and uniqueness of solution. In the present paper, we establish a convergence theory for a certain iterative algorithm to solve the implicit complementarity problem. We also demonstrate how the algorithm includes as special cases many existing iterative methods for solving a linear complementarity problem.

Abstract: An iterative aggregation procedure is described for solving large scale, finite state, finite action Markov decision processes MDPs. At each iteration, an aggregate master problem and a sequence of smaller subproblems are solved. The weights used to form the aggregate master problem are based on the estimates from the previous iteration. Each subproblem is a finite state, finite action MDP with a reduced state space and unequal row sums. Global convergence of the algorithm is proven under very weak assumptions. The proof relates this technique to other iterative methods that have been suggested for general linear programs.

Abstract: In the paper a method of designing discrete-type load-frequency regulators of a two-area reheat-type thermal system with generation-rate constraints is presented. The construction of the regulators is based on the conventional tie-line bias control. The regulator parameters are optimised by minimisirig a discrete-type quadratic performance index with a term for presenting a generation-rate constraint. The optimisation of the parameters is achieved by using a Newton-Raphson iterative algorithm. The control effects by the proposed regulators are examined by digital simulations of the system. Furthermore, a suitable means for preventing excessive and unnecessary control action is also proposed considering the constraint.

Abstract: The paper presents a new method of designing decentralised load-frequency regulators for interconnected power systems. Within the framework of this method, the interconnected mutliarea power system is decomposed into several subsystems, each of which is controlled separately by a decentralised regulator. Each subsystem consists of one area and its external equivalent in a simplified form. A decentralised control law for the study area is introduced by using a quadratic performance index. Feedback gains of the decentralised regulator, which minimise the index, are determined by a Newton-Raphson iterative algorithm. The proposed method is applied to an interconnected longitudinal 4-area system, and the effects of the proposed regulator are examined by digital simulations and associated sensitivity analysis of the system. Furthermore, a suitable means for preventing excessive control action is also considered involving a significant system nonlinearity, i.e. some generation rate constraint.

Abstract: A gradient relaxation method based on maximizing a criterion function is studied and compared to the nonlinear probabilistic relaxation method for the purpose of segmentation of images having unimodal distributions. Although both methods provide comparable segmentation results, the gradient method has the additional advantage of providing control over the relaxation process by choosing three parameters which can be tuned to obtain the desired segmentation results at a faster rate. Examples are given on two different types of scenes.

Abstract: A formal approach for the optimization of the final design of reload cores has been devised and verified. The method is based on applying the calculus of variations (Pontryagin's principle) to the normal flux and depletion system equations. The resulting set of coupled system, Euler-Lagrange (E-L), and optimality equations are solved iteratively. This is done by assuming a loading pattern for the old fuel, first solving the system equations, and then the E-L equations. The pattern is then modified by using the optimality (or Pontryagin) condition, and the process is repeated until no further improvements can be made. A computer program, OPMUV, implementing these procedures has been written and verified. The code can handle two-dimensional, quarter-core symmetric configurations with up to 241 assemblies and 4 nodes per assembly with modified one-group theory. It also has the capability of optimizing over the entire depletion cycle as well as just at the beginning of cycle (BOC). The results show that the procedure does work. In all cases tried, the method led to a reduction in nodal peaks of 1 to 3% over the final designer-obtained loading pattern within a couple of iterations. These savings carry over to comparable reductions in pin peaksmore » when the optimized patterns are used in four-group, fine-mesh calculations. Since the changes on each iteration are limited to ensure convergence, the method is thus well suited for the final fine tuning of the normally obtained patterns to gain an extra few percent in power flattening.« less

Abstract: Functional description of some parallel systems.- Alternating sequential/parallel ASP-systems.- Interface.- On direct solution of Ax = b.- Direct, parallel and ASP methods.- Iterative methods.- Special approaches for solving Ax = b on ASP.- Other problems of linear algebra.- The case study - EPOC.

Abstract: Clothoids, i.e. curves Z(s) in R2 whose curvatures x(s) are linear fitting functions of arclength s, have been used for some time for curve fitting purposes in engineering applications. The first part of the paper deals with some basic interpolation problems for clothoids and studies the existence and uniqueness of their solutions. The second part discusses curve fitting problems for clothoidal splines, i.e. C2-curves, which are composed of finitely many clothoids. An iterative method is described for finding a clothoidal spline Z(s) passing through given points Ziϵ R2 . i = 0,1,..., n+1, which minimizes the integral ∫Zx(s)2ds . This algorithm is superlinearly convergent and needs only 0(n) operations per iteration. A similar algorithm is given for a related problem of smoothing by clothoidal splines.

Abstract: An algorithm is suggested for the computation of a linear state feedback for a multi-input system such that the matrix of the resultant closed-loop system has specified eigenvalues. The algorithm is more efficient than many comparable techniques, and has some desirable numerical properties. It is also closely related to the QR algorithm for the eigenproblem.

Abstract: In this paper, we show that the iterative method of Brown and Robinson, for solving a matrix game, is also applicable to a converging sequence of matrices, where the players choose at staget a row and a column of thet-th matrix in the sequence. As an application of this result, we describe a new solution method for discounted stochastic games with finite state and action spaces.

Abstract: A successive interval test for existence and uniqueness of a solution to a nonlinear system and for convergence of iterative methods is given which is more powerful than the interval test introduced in [2] and [3].

Abstract: The method of steepest descent is applied to the solution of electrostatic problems The relation between this method and the Rayleigh-Ritz, Galerkin's, and the method of least squares is outlined Also, explicit error formulas are given for the rate of convergence for this method It is shown that this method is also suitable for solving singular operator equations In that case this method monotonically converges to the solution with minimum norm Finally, it is shown that the technique yields as a by-product the smallest eigenvalue of the operator in the finite dimensional space in which the problem is solved Numerical results are presented only for the electrostatic case to illustrate the validity of this procedure which show excellent agreement with other available data

Abstract: A man-machine interactive algorithm is given for solving multiobjective optimization problems involving one decision maker. The algorithm, a modification of the Frank-Wolfe steepest ascent method, gives at each iteration a significant freedom and ease for the decision-maker's self-expression, and requires a minimal information on his local estimate of the steepest-ascent direction. The convergence of the iterative algorithm is proved under natural assumptions on the convergence and stability of the basic Frank-Wolfe algorithm.

Abstract: We discuss in this paper a new approach to equilibrium problems in incompressible finite elasticity. This approach, which is based on the use of a convenient augmented Lagrangian functional, leads to a family of iterative methods which seem very effective for solving this type of elasticity problems once they have been approximated by appropriate finite element methods.The possibilities of the above methods are illustrated by the numerical solution of several problems in two-dimensional and axisymmetric geometries; comparisons with available analytical results are also presented.

Abstract: We review and extend results on the local convergence of the classical Newton-Kantorovich method. Then we discuss globally convergent damped and inexact Newton methods and point out advantages of using a minimal error conjugate gradient method for the linear systems arising at each Newton step.

Abstract: The present paper deals with the computational aspects of the coordination equations for hydrothermal sheduling. The hybrid method of Powell is proposed and its details are given. The method avoids possible causes for divergence encountered with the application of Newton-Raphson method. As a result a very reliable and efficient algorithm for fast solution of coordination equations emerges. Comprehensive testing of the performance of the method in comparison with Newton's is offered in the text. It is concluded that the method should be used whenever Newton's method is suspected to give doubtful performance.

Abstract: The artificial compressibility method is briefly reviewed and the effect of different forms of the artificial viscosity are studied. Successful finite element solutions of transonic airfoil problems are presented. Iterative procedures including VLSOR, Zebroid, fast solver, firstand second-degree methods, and variable acceleration parameters such as preconditioned steepest descent and conjugate gradient are discussed and necessary modifications for transonic flow computations by finite elements are implemented leading to fast, reliable, and efficient calculations.

Abstract: A method for efficiently generating a rational model of a wide-sense stationary time series is presented. In this method the autoregressive parameters associated with an ARMA model consisting of q zeros and p poles are optimally chosen with the selection being based on a finite set of time series observations. This selection is made so that a set of Yule-Walker equation approximations are ``best'' satisfied. The resultant autoregressive parameter estimates have the desired statistical feature of being unbiased and consistent. This estimation method has been found to provide a modeling performance which typically equals or exceeds that of contemporary alternatives. Moreover, this method is amenable to a computationally efficient adaptive solution procedure. The autoregressive parameters characterizing the resultant ARMA model estimate can serve the role of decision variables in pattern classification schemes. For example, these parameters can be utilized in determining whether or not a member(s) of a given signal class is contained within a noise corrupted measurement signal. This approach has been found to be particularly effective in Doppler radar and array processing applications in which one is looking for the presence of spectral lines (i.e., sinusoids) in the measurement signal.