Showing papers on "Iterative method published in 1992"

A method for registration of 3-D shapes

Abstract: The authors describe a general-purpose, representation-independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces. The method handles the full six degrees of freedom and is based on the iterative closest point (ICP) algorithm, which requires only a procedure to find the closest point on a geometric entity to a given point. The ICP algorithm always converges monotonically to the nearest local minimum of a mean-square distance metric, and the rate of convergence is rapid during the first few iterations. Therefore, given an adequate set of initial rotations and translations for a particular class of objects with a certain level of 'shape complexity', one can globally minimize the mean-square distance metric over all six degrees of freedom by testing each initial registration. One important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model, prior to shape inspection. Experimental results show the capabilities of the registration algorithm on point sets, curves, and surfaces. >

Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients

Abstract: This article describes recent technical developments that have made the total-energy pseudopotential the most powerful ab initio quantum-mechanical modeling method presently available. In addition to presenting technical details of the pseudopotential method, the article aims to heighten awareness of the capabilities of the method in order to stimulate its application to as wide a range of problems in as many scientific disciplines as possible.

The Linear Complementarity Problem

Abstract: Introduction. Background. Existence and Multiplicity. Pivoting Methods. Iterative Methods. Geometry and Degree Theory. Sensitivity and Stability Analysis. Chapter Notes and References. Bibliography. Index.

General methods for geometry and wave function optimization

Abstract: A combination of variable-metric second-order update schemes and the DIIS method for both geometry and Hartree-Fock wave function optimization is described. A recursive procedure for updating large Hessians is presented. The performances of geometry optimizations with respect to the choice of the coordinate system (symmetry-adapted, internal, and Cartesian coordinates), the initial nuclear Hessian, and the optimization procedure have been investigated by a series of benchmark molecules. Formulas for the generation of initial nuclear Hessians are given

Iterative methods by space decomposition and subspace correction

Abstract: The main purpose of this paper is to give a systematic introduction to a number of iterative methods for symmetric positive definite problems. Based on results and ideas from various existing works...

Analysis of some Krylov subspace approximations to the matrix exponential operator

Abstract: In this note a theoretical analysis of some Krylov subspace approximations to the matrix exponential operation $\exp (A)v$ is presented, and a priori and a posteriors error estimates are established. Several such approximations are considered. The main idea of these techniquesis to approximately project the exponential operator onto a small Krylov subspace and to carry out the resulting small exponential matrix computation accurately. This general approach, which has been used with success in several applications, provides a systematic way of defining high-order explicit-type schemes for solving systems of ordinary differential equations or time-dependent partial differential equations.

An adaptive clustering algorithm for image segmentation

Abstract: The problem of segmenting images of objects with smooth surfaces is considered. The algorithm that is presented is a generalization of the K-means clustering algorithm to include spatial constraints and to account for local intensity variations in the image. Spatial constraints are included by the use of a Gibbs random field model. Local intensity variations are accounted for in an iterative procedure involving averaging over a sliding window whose size decreases as the algorithm progresses. Results with an 8-neighbor Gibbs random field model applied to pictures of industrial objects, buildings, aerial photographs, optical characters, and faces show that the algorithm performs better than the K-means algorithm and its nonadaptive extensions that incorporate spatial constraints by the use of Gibbs random fields. A hierarchical implementation is also presented that results in better performance and faster speed of execution. The segmented images are caricatures of the originals which preserve the most significant features, while removing unimportant details. They can be used in image recognition and as crude representations of the image. >

Iterative procedures for reduction of blocking effects in transform image coding

Abstract: The authors propose an iterative block reduction technique based on the theory of a projection onto convex sets. The idea is to impose a number of constraints on the coded image in such a way as to restore it to its original artifact-free form. One such constraint can be derived by exploiting the fact that the transform-coded image suffering from blocking effects contains high-frequency vertical and horizontal artifacts corresponding to vertical and horizontal discontinuities across boundaries of neighboring blocks. Another constraint has to be with the quantization intervals of the transform coefficients. Specifically, the decision levels associated with transform coefficient quantizers can be used as lower and upper bounds on transform coefficients, which in turn define boundaries of the convex set for projection. A few examples of the proposed approach are presented. >

The fast multipole method (FMM) for electromagnetic scattering problems

Abstract: The fast multipole method (FMM) developed by V. Rokhlin (1990) to efficiently solve acoustic scattering problems is modified and adapted to the second-kind-integral-equation formulation of electromagnetic scattering problems in two dimensions. The present implementation treats the exterior Dirichlet problem for two-dimensional, closed, conducting objects of arbitrary geometry. The FMM reduces the operation count for solving the second-kind integral equation from O(n/sup 3/) for Gaussian elimination to O(n/sup 4/3/) per conjugate-gradient iteration, where n is the number of sample points on the boundary of the scatterer. A sample technique for accelerating convergence of the iterative method, termed complexifying k, the wavenumber, is also presented. This has the effect of bounding the condition number of the discrete system; consequently, the operation count of the entire FMM (all iterations) becomes O(n/sup 4/3/). Computational results for moderate values of ka, where a is the characteristic size of the scatterer, are given. >

A zoom feature for a dynamic programming solution to economic dispatch including transmission losses

Abstract: An iterative dynamic programming method for solving the economic dispatch problems of a system of thermal generating units including transmission line losses is presented along with a clear explanation of modifying generator cost functions during each iteration A zoom feature is applied during the iterative process in order to converge to the economic dispatch solution with low computer time and storage requirements, Dynamic programming including a short-term load forecast is briefly discussed A three-generator example is used to illustrate the method Computer memory and time requirements are presented, along with results for a 15-unit system >

An adaptive algorithm for mel-cepstral analysis of speech

Abstract: The authors describe a mel-cepstral analysis method and its adaptive algorithm. In the proposed method, the authors apply the criterion used in the unbiased estimation of log spectrum to the spectral model represented by the mel-cepstral coefficients. To solve the nonlinear minimization problem involved in the method, they give an iterative algorithm whose convergence is guaranteed. Furthermore, they derive an adaptive algorithm for the mel-cepstral analysis by introducing an instantaneous estimate for gradient of the criterion. The adaptive mel-cepstral analysis system is implemented with an IIR adaptive filter which has an exponential transfer function, and whose stability is guaranteed. The authors also present examples of speech analysis and results of an isolated word recognition experiment. >

A preconditioned iterative method for saddlepoint problems

Abstract: A preconditioned iterative method for indefinite linear systems corresponding to certain saddlepoint problems is suggested. The block structure of the systems is utilized in order to design effective preconditioners, while the governing iterative solver is a standard minimum residual method. The method is applied to systems derived from discretizations of the Stokes problem and mixed formulations of second-order elliptic problems.

How fast are nonsymmetric matrix iterations

Abstract: Three leading iterative methods for the solution of nonsymmetric systems of linear equations are CGN (the conjugate gradient iteration applied to the normal equations), GMRES (residual minimization in a Krylov space), and CGS (a biorthogonalization algorithm adapted from the biconjugate gradient iteration). Do these methods differ fundamentally in capabilities? If so, which is best under which circumstances? The existing literature, in relying mainly on empirical studies, has failed to confront these questions systematically. In this paper it is shown that the convergence of CGN is governed by singular values and that of GMRES and CGS by eigenvalues or pseudo-eigenvalues. The three methods are found to be fundamentally different, and to substantiate this conclusion, examples of matrices are presented for which each iteration outperforms the others by a factor of size $O(\sqrt N )$ or $O(N)$ where N is the matrix dimension. Finally, it is shown that the performance of iterative methods for a particular mat...

A non-linear projection method based on Kohonen's topology preserving maps

Abstract: A nonlinear projection method is presented to visualize high-dimensional data as a 2D image. The proposed method is based on the topology preserving mapping algorithm of Kohonen. The topology preserving mapping algorithm is used to train a 2D network structure. Then the interpoint distances in the feature space between the units in the network are graphically displayed to show the underlying structure of the data. Furthermore, we present and discuss a new method to quantify how well a topology preserving mapping algorithm maps the high-dimensional input data onto the network structure. This is used to compare our projection method with a well-known method of Sammon (1969). Experiments indicate that the performance of the Kohonen projection method is comparable or better than Sammon's method for the purpose of classifying clustered data. Its time-complexity only depends on the resolution of the output image, and not on the size of the dataset. A disadvantage, however, is the large amount of CPU time required. >

Deblurring subject to nonnegativity constraints

Abstract: Csiszar's I-divergence is used as a discrepancy measure for deblurring subject to the constraint that all functions involved are nonnegative. An iterative algorithm is proposed for minimizing this measure. It is shown that every function in the sequence is nonnegative and the sequence converges monotonically to a global minimum. Other properties of the algorithm are shown, including lower bounds on the improvement in the I-divergence at each step of the algorithm and on the difference between the I-difference at step k and at the limit point. A method for regularizing the solution is proposed. >

Accurate identification for control: the necessity of an iterative scheme

Abstract: If approximate identification and model-based control design are used to accomplish a high-performance control system, then the two procedures must be treated as a joint problem. Solving this joint problem by means of separate identification and control design procedures practically entails an iterative scheme. A frequency-response identification technique and a robust control design method are used to set up such an iterative scheme. Each identification step uses the previously designed controller to obtain new data from the plant. The associated identification problem has been solved by means of a coprime factorization of the unknown plant. The technique's utility is illustrated by an example. >

H-Splittings and two-stage iterative methods

Abstract: Convergence of two-stage iterative methods for the solution of linear systems is studied. Convergence of the non-stationary method is shown if the number of inner iterations becomes sufficiently large. TheR 1-factor of the two-stage method is related to the spectral radius of the iteration matrix of the outer splitting. Convergence is further studied for splittings ofH-matrices. These matrices are not necessarily monotone. Conditions on the splittings are given so that the two-stage method is convergent for any number of inner iterations.

Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy

Abstract: A fully discrete finite element method for the Cahn-Hilliard equation with a logarithmic free energy based on the backward Euler method is analysed. Existence and uniqueness of the numerical solution and its convergence to the solution of the continuous problem are proved. Two iterative schemes to solve the resulting algebraic problem are proposed and some numerical results in one space dimension are presented.

Iterative learning control: A survey and new results

Abstract: Learning control is an iterative approach to the problem of improving transient behavior for processes that are repetitive in nature. Some results on iterative learning control are presented. A complete review of the literature is given first. Then, a general formulation of the problem is given. Next, a complete analysis of the learning control problem for the case of linear, time-invariant plants and controllers is presented. This analysis offers: insight into the nature of the solution of the learning control problem by deriving sufficient convergence conditions; an approach to learning control for linear systems based on parameter estimation; and an analysis that shows that for finite-horizon problems it is possible to design a learning control algorithm that converges, with memory, in one step. Finally, a time-varying learning controller is given for controlling the trajectory of a nonlinear robot manipulator. A brief simulation example is presented to illustrate the effectiveness of this scheme. 56 refs.

Fast capacitance extraction of general three-dimensional structures

Abstract: K. Nabors and J. White (1991) presented a boundary-element-based algorithm for computing the capacitance of three-dimensional m-conductor structures whose computational complexity grows nearly as mn, where n is the number of elements used to discretize the conductor surfaces. In that algorithm, a generalized conjugate residual iterative technique is used to solve the n*n linear system arising from the discretization, and a multipole algorithm is used to compute the iterates. Several improvements to that algorithm are described which make the approach applicable and computationally efficient for almost any geometry of conductors in a homogeneous dielectric. Results using these techniques in a program which computes the capacitance of general 3D structures are presented to demonstrate that the new algorithm is nearly as accurate as the more standard direct factorization approach, and is more than two orders of magnitude faster for large examples. >

Ab initio molecular dynamics: Analytically continued energy functionals and insights into iterative solutions.

Abstract: We present a new method for performing finite-temperature ab initio total-energy calculations at long length scales, which we demonstrate with a dynamics calculation of 50 \AA{}-long phonon modes in silicon. The method involves both a prescription for the analytic continuation of tradional fermionic energy functionals into the space of nonorthonormal single-particle orbitals (speeding convergence to the minimum) and insights into the common computational physics problem of solving by iterative refinement for the state of a complex system as a function of a continuous external parameter.

Iterative asymptotic inversion in the acoustic approximation

Abstract: We propose an iterative method for the linearized prestack inversion of seismic profiles based on the asymptotic theory of wave propagation. For this purpose, we designed a very efficient technique for the downward continuation of an acoustic wavefield by ray methods. The different ray quantities required for the computation of the asymptotic inverse operator are estimated at each diffracting point where we want to recover the earth image. In the linearized inversion, we use the background velocity model obtained by velocity analysis. We determine the short wavelength components of the impedance distribution by linearized inversion of the seismograms observed at the surface of the model. Because the inverse operator is not exact, and because the source and station distribution is limited, the first iteration of our asymptotic inversion technique is not exact. We improve the images by an iterative procedure. Since the background velocity does not change between iterations. There is no need to retrace rays,...

Iteration methods for convexly constrained ill-posed problems in hilbert space

Abstract: Minimization problems in Hilbert space with quadratic objective function and closed convex constraint set C are considered In case the minimum is not unique we are looking for the solution of minimal norm If a problem is ill-posed, ie if the solution does not depend continuously on the data, and if the data are subject to errors then it has to be solved by means of regularization methods The regularizing properties of some gradient projection methods—ie convergence for exact data, order of convergence under additional assumptions on the solution and stability for perturbed data—are the main issues of this paper

A simple algorithm to achieve desired patterns for arbitrary arrays

Abstract: A simple iterative algorithm which can be used to find array weights that produce array patterns with a given look direction and an arbitrary sidelobe specification is presented. The method can be applied to nonuniform array geometries in which the individual elements have arbitrary (and differing) radiation patterns. The method is iterative and uses sequential updating to ensure that peak sidelobe levels in the array meet the specification. Computation of each successive pattern is based on the solution of a linearly constrained least-squares problem. The constraints ensure that the magnitude of the sidelobes at the locations of the previous peaks takes on the prespecified values. Phase values for the sidelobes do not change during this process, and problems associated with choosing a specific phase value are therefore avoided. Experimental evidence suggests that the procedure terminates in remarkably few iterations, even for arrays with significant numbers of elements. >

A new class of iterative methods for nonselfadjoint or indefinite problems

Abstract: A new technique is proposed to solve NSPD (nonsymmetric or indefinite) problems that are “compact” perturbations of some SPD (symmetric positive definite) problems. In the new algorithm, a direct method is first used to solve the original equation restricted on a coarser space (that has a considerably smaller dimension), then an SPD equation for the residue is solved by using one or a few iterations of a given iterative algorithm. It is shown that for any convergent iterative method for the SPD problem, the new algorithm always converges with essentially the same rate if the coarse space is properly chosen. In applications, for multiplicative domain decomposition methods, the algorithm consists of solving the original NSPD problem on the coarse mesh and solving SPD equations on all subdomains; for multigrid methods, except when the correction on the coarsest mesh is first performed for the original NSPD equation, all smoothings are carried out for SPD equations on all other levels. It is shown that most o...

Two-dimensional asymptotic iterative elastic inversion

Abstract: SUMMARY An asymptotic linearized iterative elastic inversion method is proposed to invert 2-D Earth parameters from multicomponent data and is tested numerically. The forward problem is solved by a combination of the Born approximation and ray theoretical methods. We express the perturbed seismogram in terms of perturbations of P- and S-wave impedances and density. The inversion method is based on generalized least squares. We introduce a special form of the ρ2 norm with a weighting function that corrects for geometrical spreading and obliquity of the reflectors. The Hessian for this norm could be estimated in a closed form that is asymptotically valid at high frequencies. We propose a quasi-Newtonian iterative method for the solution of the inverse problem. The first iteration of this inversion method resembles the operator proposed by Beylkin (1985) and Beylkin & Burridge (1990) for the asymptotic inversion of seismic data. Our method is more general than theirs because it can handle arbitrary discrete distributions of sources and receivers. Elastic inversion is generally ill-posed because the problem is overdetermined but undersampled. We study the resolution of the asymptotic inversion method for general sets of sources and receivers. We show that simultaneous inversion for both P- and S-wave impedance is generally ill-conditioned if data for a single scattering mode are available. In particular, it seems that only one parameter can be reliably resolved from marine data. Simultaneous inversion for a finite set of parameters can be resolved only for multicomponent elastic data containing both P-wave and S-wave information. Inversion tests using synthetic data calculated by finite-differences demonstrates that it is possible to invert simultaneously for P and S impedances.

Preconditioners for indefinite systems arising in optimization

Abstract: Methods are discussed for the solution of sparse linear equations $Ky = z$, where K is symmetric and indefinite. Since exact solutions are not always required, direct and iterative methods are both...

A Hybrid GMRES algorithm for nonsymmetric linear systems

Abstract: A new hybrid iterative algorithm is proposed for solving large nonsymmetric systems of linear equations. Unlike other hybrid algorithms, which first estimate eigenvalues and then apply this knowledge in further iterations, this algorithm avoids eigenvalue estimates. Instead, it runs GMRES until the residual norm drops by a certain factor, then re-applies the polynomial implicitly constructed by GMRES via a Richardson iteration with Leja ordering. Preliminary experiments suggest that the new algorithm frequently outperforms the restarted GMRES algorithm.