Abstract: A unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise, encompassing both the time series and the array problems, is presented. An exact expression for the ML criterion is derived in terms of the linear prediction polynomial of the signal, and an iterative algorithm for the maximization of this criterion is presented. The algorithm is equally applicable in the case of signal coherence in the array problem. Simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques. The algorithm is similar to those independently derived by Kumaresan et al. In addition to its practical value, the present formulation is used to interpret previous methods such as Prony's, Pisarenko's, and modifications thereof.

Abstract: We develop a systematic approach to the discovery of parallel iterative schemes for solving the shape-from-shading problem on a grid. A standard procedure for finding such schemes is outlined, and subsequently used to derive several new ones. The shape-from-shading problem is known to be mathematically equivalent to a nonlinear first-order partial differential equation in surface elevation. To avoid the problems inherent in methods used to solve such equations, we follow previous work in reformulating the problem as one of finding a surface orientation field that minimizes the integral of the brightness error. The calculus of variations is then employed to derive the appropriate Euler equations on which iterative schemes can be based. The problem of minimizing the integral of the brightness error term is ill posed, since it has an infinite number of solutions in terms of surface orientation fields. A previous method used a regularization technique to overcome this difficulty. An extra term was added to the integral to obtain an approximation to a solution that was as smooth as possible. We point out here that surface orientation has to obey an integrability constraint if it is to correspond to an underlying smooth surface. Regularization methods do not guarantee that the surface orientation recovered satisfies this constraint. Consequently, we attempt to develop a method that enforces integrability, but fail to find a convergent iterative scheme based on the resulting Euler equations. We show, however, that such a scheme can be derived if, instead of strictly enforcing the constraint, a penalty term derived from the constraint is adopted. This new scheme, while it can be expressed simply and elegantly using the surface gradient, unfortunately cannot deal with constraints imposed by occluding boundaries. These constraints are crucial if ambiguities in the solution of the shape-from-shading problem are to be avoided. Differrent schemes result if one uses different parameters to describe surface orientation. We derive two new schemes, using unit surface normals, that facilitate the incorporation of the occluding boundary information. These schemes, while more complex, have several advantages over previous ones.

Abstract: A comparative study of three methods for extracting solar cell parameters of the single-diode lumped-circuit model is presented. The methods compared are the curve-fitting method, an iterative 5-point method and a recently proposed analytical 5-point method. Parameter values were extracted using these three methods from experimental characteristics collected from two silicon cells over a range of illuminations and temperatures. The results show that the curve-fitting method can often give erroneous parameter values and the reasons for the errors are discussed. The 5-point methods are found to be reliable and accurate in situations where the model is a good approximation of cell performance. The analytical 5-point method, however, has the added advantage of simplicity. It is also found that for the cell measured, the single diode model is valid at illuminations above one-half AM1 but gives non-physical parameter values at lower illumination.

Abstract: 1. Discrete Iterations and Automata Networks: Basic Concepts.- 1. Discrete Iterations and Their Graphs.- 2. Examples.- 3. Connectivity Graphs and Incidence Matrices.- 4. Interpretations in Terms of Automata Networks.- 5. Serial Operation and the Gauss-Seidel Operator.- 6. Serial-Parallel Modes of Operation and the Associated Operators.- 2. A Metric Tool.- 1. The Boolean Vector Distance d.- 2. Some Basic Inequalities.- 3. First Applications.- 4. Serial-Parallel Operators. An Outline.- 5. Other Possible Metric Tools.- 3. The Boolean Perron-Frobenius and Stein-Rosenberg Theorems.- 1. Eigenelements of a Boolean Matrix.- 2. The Boolean Perron-Frobenius Theorem.- 3. The Boolean Stein-Rosenberg Theorems.- 4. Conclusion.- 4. Boolean Contraction and Applications.- 1. Boolean Contraction.- 2. A Fixed Point Theorem.- 3. Examples.- 4. Serial Mode: Gauss-Seidel Iteration for a Contracting Operator.- 5. Examples.- 6. Comparison of Operating Modes for a Contracting Operator.- 7. Examples.- 8. Rounding-Off: Successive Gauss- Seidelisations.- 9. Conclusions.- 5.Comparison of Operating Modes.- 1. Comparison of Serial and Parallel Operating Modes.- 2. Examples.- 3. Extension to the Comparison of Two Serial-Parallel Modes of Operation.- 4. Examples.- 5. Conclusions.- 6. The Discrete Derivative and Local Convergence.- 1. The Discrete Derivative.- 2. The Discrete Derivative and the Vector Distance.- 3. Application: Characterization of the Local Convergence in the Immediate Neighbourhood of a Fixed Point.- 4. Interpretation in Terms of Automata Networks.- 5. Application: Local Convergence in a Massive Neighbourhood of a Fixed Point.- 6. Gauss-Seidel.- 7. The Derivative of a Function Composition.- 8. The Study of Cycles: Attractive Cycles.- 9. Conclusions.- 7. A Discrete Newton Method.- 1. Context.- 2. Two Simple Examples.- 3. Interpretation in Terms of Automata.- 4. The Study of Convergence: The Case of the Simplified Newton Method.- 5. The Study of Convergence, The General Case.- 6. The Efficiency of an Iterative Method on a Finite Set.- 7. Numerical Experiments.- 8. Conclusions.- General Conclusion.- Appendix 2. The Number of Regular n x n Matrices with Elements in Z/p (p prime).- Appendix 4. Continuous Iterations-Discrete Iterations.- Inde.

Abstract: An explicit connection between fitting exponential models and pole-zero models to observed data is made. The fitting problem is formulated as a constrained nonlinear minimization problem. This problem is then solved using a simplified iterative algorithm. The algorithm is applied to simulated data, and the performance of the algorithm is compared to previous results.

Abstract: This paper presents an adaptive algorithm for the restoration of lost sample values in discrete-time signals that can locally be described by means of autoregressive processes. The only restrictions are that the positions of the unknown samples should be known and that they should be embedded in a sufficiently large neighborhood of known samples. The estimates of the unknown samples are obtained by minimizing the sum of squares of the residual errors that involve estimates of the autoregressive parameters. A statistical analysis shows that, for a burst of lost samples, the expected quadratic interpolation error per sample converges to the signal variance when the burst length tends to infinity. The method is in fact the first step of an iterative algorithm, in which in each iteration step the current estimates of the missing samples are used to compute the new estimates. Furthermore, the feasibility of implementation in hardware for real-time use is established. The method has been tested on artificially generated auto-regressive processes as well as on digitized music and speech signals.

Abstract: The EM method that was originally developed for maximum likelihood estimation in the context of mathematical statistics may be applied to a stochastic model of positron emission tomography (PET). The result is an iterative algorithm for image reconstruction that is finding increasing use in PET, due to its attractive theoretical and practical properties. Its major disadvantage is the large amount of computation that is often required, due to the algorithm's slow rate of convergence. This paper presents an accelerated form of the EM algorithm for PET in which the changes to the image, as calculated by the standard algorithm, are multiplied at each iteration by an overrelaxation parameter. The accelerated algorithm retains two of the important practical properties of the standard algorithm, namely the selfnormalization and nonnegativity of the reconstructed images. Experimental results are presented using measured data obtained from a hexagonal detector system for PET. The likelihood function and the norm of the data residual were monitored during the iterative process. According to both of these measures, the images reconstructed at iterations 7 and 11 of the accelerated algorithm are similar to those at iterations 15 and 30 of the standard algorithm, for two different sets of data. Important theoretical properties remain to be investigated, namely the convergence of the accelerated algorithm and its performance as a maximum likelihood estimator.

Abstract: : The combination of iterative methods with preconditionings based on incomplete LU factorizations constitutes an effective class of methods for solving the sparse linear systems arising from the discretization of elliptic partial differential equations. In this paper, we show that there are some settings in which the incomplete LU preconditioners are not effective, and we demonstrate that their poor performance is due to numerical instability. Our analysis consists of an analytic and numerical study of a sample two-dimensional non-self-adjoint elliptic problem discretized by several finite difference schemes. (Author)

Abstract: Iterative methods for solving a square system of nonlinear equations g(x) = 0 often require that the sum of squares residual γ (x) ≡ ½∥g(x)∥2 be reduced at each step. Since the gradient of γ depends on the Jacobian ∇g, this stabilization strategy is not easily implemented if only approximations Bk to ∇g are available. Therefore most quasi-Newton algorithms either include special updating steps or reset Bk to a divided difference estimate of ∇g whenever no satisfactory progress is made. Here the need for such back-up devices is avoided by a derivative-free line search in the range of g. Assuming that the Bk are generated from an rbitrary B0 by fixed scale updates, we establish superlinear convergence from within any compact level set of γ on which g has a differentiable inverse function g−1.

Abstract: The issue of testing two-dimensional iterative arrays with a constant number of test vectors independent of the array size (C-testability) is discussed in this paper. Sufficient conditions for C-testability are stated. It is shown that any two-dimensional array can be modified to become C-testable. An extension to systolic (synchronous) arrays is made. The approach simplifies testing systolic arrays by using one test vector to test many cells of the array in a periodic fashion. A two-dimensional array for matrix multiplication is used to illustrate the approach for systolic arrays.

Abstract: The merits and limitations of some existing procedures for the solution of contact problems, modeled by the finite element method, are examined. Based on the Lagrangian multiplier method, a partitioning scheme can be used to obtain a small system of equation for the Lagrange multipliers which is then solved by the conjugate gradient method. A two-level contact algorithm is employed which first linearizes the nonlinear contact problem to obtain a linear contact problem that is in turn solved by the Newton method. The performance of the algorithm compared to some existing procedures is demonstrated on some test problems.

Abstract: This paper presents an efficient method for the calculation of the inverse dynamic model of robots. The given method reduces significantly the computational burden such that the inverse dynamics can be computed on real time at servo rate. The method leads almost directly to models with minimum number of arithmetic operations. The method is based on Newton-Euler formulation, on an iterative symbolic procedure and on an analysis of the links inertial parameters which leads to condensate their number by eliminating and regrouping some of them. A FORTRAN program has been developed to generate automatically the dynamic models of open chain robots.

Abstract: We present an iterative method for solving large sparse nonsymmetric linear systems of equations that enhances Manteuflel’s adaptive Chebyshev method with a conjugate gradient-like method. The new method replaces the modified power method for computing needed eigenvalue estimates with Arnoldi’s method, which can be used to simultaneously compute eigenvalues and to improve the approximate solution. Convergence analysis and numerical experiments suggest that the method is more efficient than the original adaptive Chebyshev algorithm.

Abstract: The Defect Correction Approach.- Historical Examples of Defect Correction.- General Defect Correction Principles.- Discretization of Operator Equations.- Defect Correction and Discretization.- Multi-level and Multi-grid Methods.- References.- Defect Correction for Operator Equations.- Defect Correction Algorithms for Stiff Ordinary Differential Equations.- Specification of the Algorithm.- Previous Results.- The Concept of B-Convergence.- B-Convergence Properties of Certain IDeC-Algorithms.- References.- On a Principle of Direct Defect Correction Based on A-Posteriori Error Estimates.- Basic Relations Between Defect Corrections and Asymptotic Expansions.- Defect Corrections Through Projection Methods.- Direct Defect Correction via Finite Element Methods for Singularly Perturbed Differential Equations.- References.- Simultaneous Newton's Iteration for the Eigenproblem.- The Sylvester Equation AX?XB= C.- A Quadratic Equation for the Invariant Subspace.- Newton's Method on (7).- Simplified Newton's Method.- Modified Newton's Methods.- Conclusion.- References.- On Some Two-level Iterative Methods.- The General Two-level Iterative Process.- Applications to Integral Equations.- Projection-iterative Methods.- Iterative Aggregation Methods.- Conclusion.- References.- Multi-grid Methods.- Local Defect Correction Method and Domain Decomposition Techniques.- Defect Correction Method.- Local Defect Correction (Algorithm Numerical Examples of the Local Defect Correction Error Estimates Multi-grid Iteration with Local Defect Correction).- Domain Decomposition Methods.- References.- Fast Adaptive Composite Grid (FAC) Methods: Theory for the Variational Case.- Two-level Methods.- Remarks.- References.- Mixed Defect Correction Iteration for the Solution of a Singular Perturbation Problem.- Local Mode Analysis.- The Defect Correction Principle.- The Mixed Defect Correction Process (MDCP).- Local Mode Analysis for the MDCP Solution.- The Convergence of the MDCP Iteration.- Boundary Analysis of the MDCP Solutions.- Numerical Examples.- References.- Computation of Guaranteed High-accuracy Results.- Solution of Linear and Nonlinear Algebraic Problems with Sharp, Guaranteed Bounds.- Computer Arithmetic.- Inclusion Methods for Linear Systems.- Implementation of Inclusion Algorithms.- Nonlinear Systems.- Conclusion.- References.- Residual Correction and Validation in Functoids.- Functoids and Roundings.- Iterative Residual Correction.- References.- Defect Corrections in Applied Mathematics and Numerical Software.- Defect Corrections and Hartree-Fock Method.- Hartree-Fock Method.- Defect Corrections on Infinite Intervals.- Asymptotic Boundary Conditions and Defect Corrections with Changing Boundary Points.- References.- Deferred Corrections Software and Its Application to Seismic Ray Tracing.- Discontinuous Interfaces at Known Locations.- PASVA4, Part I.- Discontinuities at Unknown Locations.- PASVA4, Part II. Algebraic Parameters and Conditions.- Three-dimensional Two-point Ray Tracing.- Future Developments.- References.- Numerical Engineering: Experiences in Designing PDE Software with Selfadaptive Variable Step Size/Variable Order Difference Methods.- Estimate of the Truncation Error.- The Error Equation.- The Ordinary BVP.- 2- and 3-D Elliptic PDE's.- The Ordinary IVP.- Parabolic PDE's.- Three Examples.- Concluding Remarks.- References.

Abstract: Optical-correlation filters that are translationally and rotationally invariant are made target specific by incorporating all the angular harmonics of the target image. An iterative design method similar to the technique of convex projections allows the image angular harmonics to be rephased so that the filter exhibits a constant-amplitude rotational response. Rotating this filter in the Fourier plane forms the Fourier summation of all angular harmonics of the input image. Ari image to be detected must have angular-harmonic terms that have an amplitude and a phase that are keyed exactly to the target image. This lock-and-tumbler filter exhibits excellent discrimination capability while preserving rotational invariance.

Abstract: An iterative procedure in the frequency domain is presented for flutter analysis of large dynamic systems with multiple structural nonlinearities. The major components of the procedure are the describing function approach for system linearization, a structural dynamics modification method for shifting system mode shapes and frequencies, and a complex eigenvalue algorithm for solution of the flutter equation. The purpose of the procedure is to achieve alignment of the oscillatory amplitude in each nonlinear spring with the describing function prediction of stiffness before computing the final stability characteristics. The result is a system tuned to the flutter frequency at the time of instability. To support the development and validation of the procedure, several describing functions are formulated and a quantitative measure of the errors in each is presented. Validation of the iterative method is accomplished through examples involving dynamic systems of increasing complexity, coupled with various representations of the unsteady aerodynamic forces. Both numerical simulations and experimental data are used to compare with the iterative predictions. In the cases studied, the agreement is good to excellent, with the method accurately predicting the amplitude of a limit cycle flutter as well as the initial disturbance required to produce flutter.

Abstract: A computational approach to limit solutions is considered most challenging for two major reasons. A limit solution is likely to be non-smooth such that certain non-differentiable functions are perfectly admissible and make physical and mathematical sense. Moreover, the possibility of non-unique solutions makes it difficult to analyze the convergence of an iterative algorithm or even to define a criterion of convergence. In this paper, we use two mathematical tools to resolve these difficulties. A duality theorem defines convergence from above and from below the exact solution. A combined smoothing and successive approximation applied to the upper bound formulation perturbs the original problem into a smooth one by a small parameter e. As e → 0, the solution of the original problem is recovered. This general computational algorithm is robust such that from any initial trial solution, the first iteration falls into a convex hull that contains the exact solution(s) of the problem. Unlike an incremental method thut invariably renders the limit problem ill-conditioned, the algorithm is numerically stable. Limit analysis itself is a highly efficient concept which bypasses the tedium of the intermediate elastic-plastic deformation and seeks the most important information directly. With the said algorithm, we have produced many limit solutions of plane stress problems. Certain non-smooth characters of the limit solutions are shown in the examples presented. Two well-known as well as one parametric family of yield functions are used to allow comparison with some classical solutions.

Abstract: A variety of identification procedures exists for estimating the parameters of an autoregressive moving-average (ARMA) process from noise-free excitation and noise-contaminated response data. In this paper, an identification procedure is proposed for the more realistic situation in which both the excitation and response are contaminated by white noises. The method is based upon the null space characterization of an associated "data matrix." Some of the more important algebraic properties possessed by this data matrix are first established in the ideal noise-free data case. In particular, it is found that an overordering of the ARMA model will not impair the identification of the Underlying system. In the more realistic noise-contaminated data case, an approximation of the data matrix's null space is affected by using an eigenvalue-eigenvector decomposition. By incorporating this null space approximation, the deleterious effects of the noise are significantly reduced thereby giving rise to improved modeling performance. This improvement is demonstrated by means of a standard example in which the proposed identification method is shown to produce a better modeling behavior than does the classical least-squares method, the corresponding iterative generalized least-squares method, and a commonly employed instrumental variable method.

Abstract: In this paper we develop multi-grid algorithms for the numerical solution of Hamilton-Jacobi-Bellman equations The proposed schemes result from a combination of standard multi-grid techniques and the iterative methods used by Lions and mercier in [11] A convergence result is given and the efficiency of the algorithms is illustrated by some numerical examples

Abstract: An iterative procedure based on the conjugate gradient method is used to solve a variety of matrix equations representing electromagnetic scattering problems, in an attempt to characterize the typical rate of convergence of that method. It is found that this rate depends on the cell density per wavelength used in the discretization, the presence of symmetries in the solution, and the degree to which mixed cell sizes are used in the models. Assuming cell densities used in the discretization are in the range of ten per linear wavelength, the iterative algorithm typically requires N/4 to N/2 steps to converge to necessary accuracy, where N is the order of the matrix under consideration.

Abstract: Systems of linear algebraic equations must be solved at each integration step in all commonly used methods for the numerical solution of systems of stiff IVPs for ODES. Frequently, a substantial portion of the total computational-work and storage required to solve stiff IVPs is devoted to solving these linear algebraic systems, particularly if the systems are large. Over the past decade, several efficient iterative methods have been developed to solve large sparse (nonsymmetric) systems of linear algebraic equations. We study the use of a class of these iterative methods in codes for stiff IVPs. Our theoretical estimates and preliminary numerical results show that the use of iterative linear-equation solvers in stiff-ODE codes improves the efficiency—in terms of both computational—work and storage-with which a significant class of stiff IVPs having large sparse Jacobians can be solved.

Abstract: Completely flexible grid block connections are necessary for local mesh refinement and modelling of faults and pinchouts For practical purposes, it is necessary to combine such arbitrary connectivity with an adaptive implicit technique In this paper, the methods used to discretize the flow equations for unusual geometries is discussed, and a rigorous analysis is given A completely general sparse incomplete LU iterative solver is described which can solve Jacobians with arbitrary connectivity Various test results are presented

Abstract: The one-dimensional wave equation in a layered medium is considered. The inverse problem consists of computing the acoustic impedance of the layered medium from the reflection response measured at the surface. For a discrete medium consisting of homogeneous layers of equal traveltime the Levinson algorithm is used to compute the reflection coefficients at the interfaces between the layers. For a medium with continuously varying parameters, an iterative frequency-domain method based on the Riccati equation is used. When these methods are applied to band-limited synthetic seismic data, the result is a filtered version of the acoustic impedance. When the noise level is increased, both methods diverge. For a medium consisting of homogeneous layers of unknown thickness, the reflection coefficients and the traveltimes are estimated simultaneously by using a detection scheme combined with a numerical solution of the wave equation. The performance of three different methods were compared on synthetic data. The first method is based on downward continuation of the upgoing and downgoing wavefield. The second method is based on the computation of the wavefield at the surface, and progressively removing the effect of the layers once they have been identified. The third method is based on layer removal in the frequency domain. In all these cases, the seismic pulse was assumed to be known, and the same detection scheme was used. Numerical simulations indicate that, with the detection scheme used, the method based on surface calculations gave slightly better results than the method using downward continuation. Both these methods gave improved results compared to the layer removal scheme when applied to data with medium noise level. All three detection methods proved to have superior performance compared to the classical method using the Levinson algorithm or the iterative frequency-domain method. For small noise levels, the detection methods all gave a very good reconstruction of the acoustic impedance. For medium and high noise levels, the detection methods remained stable, although a number of false reflectors were found.

Abstract: This paper is concerned with the problem of optimal power flow in a hydro-thermal electric power system (HTOPF). The formulation and optimality conditions for systems with fixed head hydro-plants subject to an energy limited constraint are presented. The solution to obtain the optimal operational strategy is implemented using Newton's method. Due to the large scale nature of the problem, special sparsity oriented and structural property enhancements are explored and four versions for algorithmic implementation are detailed in the paper. Special attention is paid to finding realistic initial guess estimates for the algorithms reported. Results of computational experience with six standard test systems are reported in the paper.