Abstract: This paper presents two partition methods that speed up iterative search methods applied to vehicle routing problems including a large number of vehicles. Indeed, using a simple implementation of taboo search as an iterative search method, every best-known solution to classical problems was found. The first partition method (based on a partition into polar regions) is appropriate for Euclidean problems whose cities are regularly distributed around a central depot. The second partition method is suitable for any problem and is based on the arborescence built from the shortest paths from any city to the depot. Finally, solutions that are believed to be optimum are given for problems generated on a grid. © 1993 by John Wiley & Sons, Inc.

Abstract: A method for Bayesian reconstruction which relies on updates of single pixel values, rather than the entire image, at each iteration is presented. The technique is similar to Gauss-Seidel (GS) iteration for the solution of differential equations on finite grids. The computational cost per iteration of the GS approach is found to be approximately equal to that of gradient methods. For continuously valued images, GS is found to have significantly better convergence at modes representing high spatial frequencies. In addition, GS is well suited to segmentation when the image is constrained to be discretely valued. It is shown that Bayesian segmentation using GS iteration produces useful estimates at much lower signal-to-noise ratios than required for continuously valued reconstruction. The convergence properties of gradient ascent and GS for reconstruction from integral projections are analyzed, and simulations of both maximum-likelihood and maximum a posteriori cases are included. >

Abstract: A new algorithm using the primal-dual interior point method with the predictor-corrector for solving nonlinear optimal power flow (OPF) problems is presented. The formulation and the solution technique are new. Both equalities and inequalities in the OPF are considered and simultaneously solved in a nonlinear manner based on the Karush-Kuhn-Tucker (KKT) conditions. The major computational effort of the algorithm is solving a symmetrical system of equations, whose sparsity structure is fixed. Therefore only one optimal ordering and one symbolic factorization are involved. Numerical results of several test systems ranging in size from 9 to 2423 buses are presented and comparisons are made with the pure primal-dual interior point algorithm. The results show that the predictor-corrector primal-dual interior point algorithm for OPF is computationally more attractive than the pure primal-dual interior point algorithm in terms of speed and iteration count. >

Abstract: A model for data acquired with the use of a charge-coupled-device camera is given and is then used for developing a new iterative method for restoring intensities of objects observed with such a camera. The model includes the effects of point spread, photoconversion noise, readout noise, nonuniform flat-field response, nonuniform spectral response, and extraneous charge carriers resulting from bias, dark current, and both internal and external background radiation. An iterative algorithm is identified that produces a sequence of estimates converging toward a constrained maximum-likelihood estimate of the intensity distribution of an imaged object. An example is given for restoring images from data acquired with the use of the Hubble Space Telescope.

Abstract: An algorithm is presented for iterative learning of the control input for a linear discrete-time multivariable system. Necessary and sufficient conditions are stated for convergence of the proposed algorithm. The algorithm synthesis and analysis are based on two-dimensional (2-D) system theory. A numerical example is given. >

Abstract: A class of iterative methods for solving the blind deconvolution problem, i.e. for recovering the input of an unknown possibly nonminimum-phase linear system by observation of its output, is presented. These methods are universal do not require prior knowledge of the input distribution, are computationally efficient and statistically stable, and converge to the desired solution regardless of initialization at a very fast rate. The effects of finite length of the data, finite length of the equalizer, and additive noise in the system on the attainable performance (intersymbol interference) are analyzed. It is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems. Recursive and sequential algorithms are also developed, which allow real-time implementation and adaptive equalization of time-varying systems. >

Abstract: The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. An implementation is presented of a look-ahead version of the Lanczos algorithm that, except for the very special situation of an incurable breakdown, overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products as the standard Lanczos process without look-ahead.

Abstract: SUMMARY We have developed an inversion procedure that uses conjugate gradient relaxation methods. Although one can generalize the method to all inverse problems, we demonstrate its use to invert magnetotelluric data for 3-D earth models. This procedure allows us to bypass the actual computation of the sensitivity matrix A or the inversion of the ATA term. In fact, with the relaxation approach, one only needs to compute the effect of the sensitivity matrix or its transpose multiplying an arbitrary vector. We show that each of these requires one forward problem with a distributed set of sources either in the volume (for A multiplying a vector) or on the surface (for AT multiplying a vector). This significantly reduces the computational requirements needed to do a 3-D inversion. For this paper, we have simplified the boundary conditions by assuming the model is repeated in the horizontal directions, but this is not a necessary constraint of the method. The algorithm reduces data errors to the 2 per cent level for noise-free synthetic 3-D magnetotelluric data.

Abstract: Two algorithms are introduced that show exceptional promise in finding molecular conformations using distance geometry on nuclear magnetic resonance data. The fist algorithm is a gradient version of the majorization algorithm from multidimensional scaling. The main contribution is a large decrease in CPU time. The second algorithm is an iterative algorithm between possible conformations obtained from the fist al- gorithm and permissible data points near the configuration. These ideas are similar to alternating least squares or alternating projections on convex sets. The iterations significantly improve the conformation from the first algorithm when applied to the small peptide

Abstract: Proposes a shift-invariant multiresolution representation of signals or images using dilations and translations of the autocorrelation functions of compactly supported wavelets. Although these functions do not form an orthonormal basis, their properties make them useful for signal and image analysis. Unlike wavelet-based orthonormal representations, the present representation has (1) symmetric analyzing functions, (2) shift-invariance, (3) associated iterative interpolation schemes, and (4) a simple algorithm for finding the locations of the multiscale edges as zero-crossings. The authors also develop a noniterative method for reconstructing signals from their zero-crossings (and slopes at these zero-crossings) in their representation. This method reduces the reconstruction problem to that of solving a system of linear algebraic equations. >

Abstract: The determination of the direct kinematics of fully parallel manipulators is in general a difficult problem but has to be solved for any practical use. Various methods are presented to solve this problem: two kinds of iterative schemes, a reduced iterative scheme, and a polynomial method. The computation time of these methods are compared and their various advantages are shown. >

Abstract: A comprehensive study of the general l/sub 1/-optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented. By formulating the interpolation conditions in a concise and natural way, the general theory is developed in simpler terms and with a minimum number of assumptions. In addition, further insight is gained into the structure of the optimal solution, and different classes of multiblock problems are distinguished. This leads to a conceptually attractive, iterative method for finding approximate solutions. >

Abstract: In this paper, we show that the general variational inequality problem is equivalent to solving the Wiener-Hopf equations. We use this equivalence to suggest and analyze a number of iterative algorithms for solving general variational inequalities. We also discuss the convergence criteria for these algorithms.

Abstract: Moment method calculations have the well-known limitations of requiring excessive storage and execution times for even modestly large electromagnetics problems. The impedance matrix localization (IML) method was introduced as a modification to standard moment method calculations to ease these limitations. It utilizes a matrix transformation which effectively changes the basis (testing) functions into ones resembling traveling waves. An improved method that uses an orthogonal transformation to generate standing-wave-like basis functions is presented here. Remarkable improvements are achieved in the numerical stability of the method and in its compatibility with iterative solvers. Furthermore, the correspondence of the large elements in this matrix to geometrical theory of diffraction (GTD) terms is strengthened, as is the possibility of further increasing the speed of iterative solutions by constructing preconditioners based on the pattern of nonzero matrix elements. >

Abstract: Slab derived scatter estimation (SDSE) accurately models the asymmetric, spatially varying scatter response function in uniformly attenuating objects with convex surfaces. This model is implemented in a projector-backprojector that, when combined with iterative reconstruction techniques, provides accurate scatter compensation in single-photon emission computed tomography (SPECT). These iterative reconstruction-based scatter compensation techniques have the advantage that they use all detected photons, avoiding the noise amplification occurring with subtraction based schemes. Scatter compensation with iterative reconstruction does not involve the use of arbitrary adjustable parameters. A new fast algorithm for implementing SDSE that reduces computation time by a factor of 16 compared to a direct implementation is presented. Projection data computed with the new algorithm compare well with data from Monte Carlo simulations. >

Abstract: A general procedure for the design of analysis-synthesis systems based on nonuniform filter banks is described. The procedure is based on a time-domain analysis of nonuniform systems, which results in a set of conditions for the exact reconstruction of the input signal at the output. These conditions are used as part of a powerful iterative algorithm for designing finite impulse response (FIR) filter banks with an arbitrary nonuniform frequency resolution. This new framework permits the design of systems with arbitrary rational decimation rates in different bands. Systems based on maximally or nonmaximally decimated filter banks, on low and minimum delay systems, and on block decimators are also among the systems that can be designed using this method. >

Abstract: The performance of the Born iterative method of nonlinear two-dimensional profile inversion is examined for the reconstruction of large objects and in the presence of measurement noise. Time-domain data are used. It is shown that objects at least as large as about nine wavelengths can be inverted without any convergence problems. The algorithm is shown to perform well in the presence of 10% noise, or 20-dB signal-to-noise ratio. The simultaneous inversion of permittivity and conductivity profiles is formulated and solved using the Born iterative method. Objects with various loss tangents are reconstructed, and the limits of applicability of the algorithm are investigated. >

Abstract: An iterative algorithm for calibration of a robotic hand-eye relationship is presented. The hand-eye calibration can be performed by solving a system of homogeneous transformation equations of the form A/sub i/X=XB/sub i/, where X is the unknown sensor position relative to the robot wrist, A/sub i/ is the ith robot motion, and B/sub i/ is the ith sensor motion. Unlike existing approaches, the algorithm presented solves the kinematic parameters of X in one stage, thus eliminating error propagation and improving noise sensitivity. Furthermore, with the iterative algorithm, the parameters of X can be computed even when the rotational part of B/sub i/ is unknown. This is important since position is easier to measure than orientation. Comparative simulation studies show that the performance of the iterative algorithm is usually better than that of noniterative two-stage algorithms, regardless of whether the orientation part of B/sub i/ is used or not. This paper also discusses the application of the proposed method to calibration of a tool mounted on a robot manipulator. >

Abstract: We describe a new algorithm for computing eigenvalues, spectral intensities, and selected eigenvectors of multidimensional vibrational potential surfaces. The method involves a synthesis of pseudospectral and sequential adiabatic reduction methods and merges the storage and computational advantages of the former with the improved basis set generated by the latter. The recursive residue generation method, which utilizes a Lanczos‐based diagonalization procedure, is employed to calculate the observables. As a test case, we apply the method to computation of the infrared and stimulated emission pumping spectra for the HCN molecule and demonstrate a very large (one to three orders of magnitude) reduction in computational effort (for comparable accuracy) as compared to discrete variable representation (DVR)/adiabatic reduction or standard collocation approaches. We expect that this advantage will be increased considerably for larger (e.g., tetra‐atomic) systems and will permit accurate basis set calculations on such systems to be carried out in a straightforward fashion.

Abstract: Using the very-dishonest Newton method as the base, Gauss, Newton and relaxed-Newton type parallel algorithms are discussed and compared with solution data obtained using the iPSC-2 32 node hypercube, and the Alliant FX-8 and Sequent/Symmetry (26 CPUs) shared-memory machines. The bottlenecks in both algorithm and implementation are described in some detail. Various techniques and in particular their potential bottlenecks when using large-scale parallel processing are also discussed. A new parallel algorithm, the Maclaurin-Newton method (MNM), is used for stability analysis for the first time. The implementation of this method for the dynamic analysis is discussed, and it is compared to other methods. The advantage of the MNM is that it is completely parallel while retaining some Newton-type convergence characteristics. The relaxed-Newton-type algorithms are shown to be the most effective. A toroidal method (or traveling window technique) is adopted for parallel-in-space and -in-time implementation. Some comments on the improvement and its limitations are provided. >

Abstract: An iterative instantaneous frequency (IF) estimation scheme is presented in which successive IF estimates are obtained from the peak of the cross Wigner-Ville distribution (XWVD), using a reference signal synthesized from an initial IF estimate. Theoretical and practical aspects of performance are discussed, and the performance is compared with that of other methods. >

Abstract: An iterative optimization algorithm for designing laser fields to control molecular motion which utilizes laboratory input (test fields) and output (resulting product yields) information is proposed. Laboratory uncertainties such as laser field noise and limited precision in the product yield measurements are included in the simulations of the experiments. Two simulated examples of implementation of the algorithm are presented: selective electronic excitation in a model four‐state system and maximizing dissociation yield of the hydrogen fluoride molecule. Both examples demonstrate that, even with the inclusion of laboratory uncertainties, the experimental learning‐based algorithm is a potentially feasible method of controlling molecular motion and possibly manipulating chemical reactions.

Abstract: The EM algorithm is a popular iterative method for finding the maximum likelihood estimate when the likelihood function is either non-analytical or its functional form is too difficult to maximize directly. In this paper we analyze the convergence properties of the EM algorithm. By representing the E step in a Taylor series with remainder we obtain a derivation of region of convergence and asymptotic convergence rates for a specified complete data space. These results can help one tailor the choice of complete data space so as to achieve an optimal tradeoff between ease of implementation and rapid convergence of the EM algorithm.