Showing papers on "Iterative method published in 1991"

QMR: a quasi-minimal residual method for non-Hermitian linear systems

Abstract: The biconjugate gradient (BCG) method is the "natural" generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. In this paper, we present a novel BCG-like approach, the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported.

FastCap: a multipole accelerated 3-D capacitance extraction program

Abstract: A fast algorithm for computing the capacitance of a complicated three-dimensional geometry of ideal conductors in a uniform dielectric is described and its performance in the capacitance extractor FastCap is examined. The algorithm is an acceleration of the boundary-element technique for solving the integral equation associated with the multiconductor capacitance extraction problem. The authors present a generalized conjugate residual iterative algorithm with a multipole approximation to compute the iterates. This combination reduces the complexity so that accurate multiconductor capacitance calculations grow nearly as nm, where m is the number of conductors. Performance comparisons on integrated circuit bus crossing problems show that for problems with as few as 12 conductors the multipole accelerated boundary element method can be nearly 500 times faster than Gaussian-elimination-based algorithms, and five to ten times faster than the iterative method alone, depending on required accuracy. >

Parallel and deterministic algorithms from MRFs: surface reconstruction

Abstract: Deterministic approximations to Markov random field (MRF) models are derived. One of the models is shown to give in a natural way the graduated nonconvexity (GNC) algorithm proposed by A. Blake and A. Zisserman (1987). This model can be applied to smooth a field preserving its discontinuities. A class of more complex models is then proposed in order to deal with a variety of vision problems. All the theoretical results are obtained in the framework of statistical mechanics and mean field techniques. A parallel, iterative algorithm to solve the deterministic equations of the two models is presented, together with some experiments on synthetic and real images. >

Inverse scattering: an iterative numerical method for electromagnetic imaging

Abstract: The authors propose a spatial iterative algorithm for electromagnetic imaging based on a Newton-Kantorovich procedure for the reconstruction of the complex permittivity of inhomogeneous lossy dielectric objects with arbitrary shape. Starting from integral representation of the electric field and using the moment method, this technique has been developed for 2-D (for TM and TE polarization cases) objects as well as for 3-D objects. Its performance has been compared with spectral techniques of classical diffraction tomography, the modified Newton method, and the pseudo-inverse method. >

Iterative solution of linear systems

Abstract: Recent advances in the field of iterative methods for solving large linear systems are reviewed. The main focus is on developments in the area of conjugate gradient-type algorithms and Krylov subspace methods for non-Hermitian matrices.

Nonlinear multilevel models, with an application to discrete response data

Abstract: SUMMARY A procedure is proposed for the analysis of multilevel nonlinear models using a linearization. The case of log linear models for discrete response data is studied in detail. Nonlinear models arise in a number of circumstances, notably when modelling discrete data. In this paper we consider the multilevel nonlinear model. As in linear multilevel models, we shall consider the general case where any of the model coefficients can be random at any level, and where the random parameters may also be specified functions of the fixed parameter estimates, discussed by H. Goldstein, R. Prosser and J. Rasbash in an as yet unpublished report. In the next two sections we set out the model and define notation; this is followed by a section on estimation and then some examples.

Static rate-optimal scheduling of iterative data-flow programs via optimum unfolding

Abstract: Rate-optimal compile-time multiprocessor scheduling of iterative dataflow programs suitable for real-time signal processing applications is discussed. It is shown that recursions or loops in the programs lead to an inherent lower bound on the achievable iteration period, referred to as the iteration bound. A multiprocessor schedule is rate-optimal if the iteration period equals the iteration bound. Systematic unfolding of iterative dataflow programs is proposed, and properties of unfolded dataflow programs are studied. Unfolding increases the number of tasks in a program, unravels the hidden concurrently in iterative dataflow programs, and can reduce the iteration period. A special class of iterative dataflow programs, referred to as perfect-rate programs, is introduced. Each loop in these programs has a single register. Perfect-rate programs can always be scheduled rate optimally (requiring no retiming or unfolding transformation). It is also shown that unfolding any program by an optimum unfolding factor transforms any arbitrary program to an equivalent perfect-rate program, which can then be scheduled rate optimally. This optimum unfolding factor for any arbitrary program is the least common multiple of the number of registers (or delays) in all loops and is independent of the node execution times. An upper bound on the number of processors for rate-optimal scheduling is given. >

A regularized iterative image restoration algorithm

Abstract: The development of the algorithm is based on a set theoretic approach to regularization. Deterministic and/or statistical information about the undistorted image and statistical information about the noise are directly incorporated into the iterative procedure. The restored image is the center of an ellipsoid bounding the intersection of two ellipsoids. The proposed algorithm, which has the constrained least squares algorithm as a special case, is extended into an adaptive iterative restoration algorithm. The spatial adaptivity is introduced to incorporate properties of the human visual system. Convergence of the proposed iterative algorithms is established. For the experimental results which are shown, the adaptively restored images have better quality than the nonadaptively restored ones based on visual observations and on an objective criterion of merit which accounts for the noise masking property of the visual system. >

Discrete all-pole modeling

Abstract: A method for parametric modeling and spectral envelopes when only a discrete set of spectral points is given is introduced. This method, called discrete all-pole (DAP) modeling, uses a discrete version of the Itakura-Saito distortion measure as its error criterion. One result is an autocorrelation matching condition that overcomes the limitations of linear prediction and produces better fitting spectral envelopes for spectra that are representable by a relatively small discrete set of values, such as in voiced speech. An iterative algorithm for DAP modeling that is shown to converge to a unique global minimum is presented. Results of applying DAP modeling to real and synthetic speech are also presented. DAP modeling is extended to allow frequency-dependent weighting of the error measure, so that spectral accuracy can be enhanced in certain frequency regions. >

Motion planning for controllable systems without drift

Abstract: A general strategy for solving the motion planning problem for real analytic, controllable systems without drift is proposed. The procedure starts by computing a control that steers the given initial point to the desired target point for an extended system, in which a number of Lie brackets of the system vector fields are added. Using formal calculations with a product expansion relative to P. Hall basis, another control is produced that achieves the desired result on the formal level. This provides an exact solution of the original problem if the given system is nilpotent. For a general system, an iterative algorithm is derived that converges very quickly to a solution. For nonnilpotent systems which are feedback nilpotentizable, the algorithm, in cascade with a precompensator, produces an exact solution. Results of simulations which illustrate the effectiveness of the procedure are presented. >

Optimal partitioning for classification and regression trees

Abstract: An iterative algorithm that finds a locally optimal partition for an arbitrary loss function, in time linear in N for each iteration is presented. The algorithm is a K-means-like clustering algorithm that uses as its distance measure a generalization of Kullback's information divergence. Moreover, it is proven that the globally optimal partition must satisfy a nearest neighbour condition using divergence as the distance measure. These results generalize similar results of L. Breiman et al. (1984) to an arbitrary number of classes or regression variables and to an arbitrary number of bills. Experimental results on a text-to-speech example are provided and additional applications of the algorithm, including the design of variable combinations, surrogate splits, composite nodes, and decision graphs, are suggested. >

Interval arithmetic in power flow analysis

Abstract: Power flow analysis is the fundamental tool for the study of power systems. The data for this problem are subject to uncertainty. Interval arithmetic is used to solve the power flow problem. Interval arithmetic takes into consideration the uncertainty of the nodal information, and is able to provide strict bounds for the solutions to the problem: all possible solutions are included within the bounds given by interval arithmetic. Results are compared with those obtainable by Monte Carlo simulations and by the use of stochastic power flows. Object-oriented programming techniques makes it possible to use interval arithmetic with minimal modifications to existing software. However, to reduce the conservatism inherent in all interval arithmetic computations, an iterative method is used to obtain the hull of the solution set. >

Constrained iterative speech enhancement with application to speech recognition

Abstract: The basis of an improved form of iterative speech enhancement for single-channel inputs is sequential maximum a posteriori estimation of the speech waveform and its all-pole parameters, followed by imposition of constraints upon the sequence of speech spectra. The approaches impose intraframe and interframe constraints on the input speech signal. Properties of the line spectral pair representation of speech allow for an efficient and direct procedure for application of many of the constraint requirements. Substantial improvement over the unconstrained method is observed in a variety of domains. Informed listener quality evaluation tests and objective speech quality measures demonstrate the technique's effectiveness for additive white Gaussian noise. A consistent terminating point of the iterative technique is shown. The current systems result in substantially improved speech quality and linear predictive coding (LPC) parameter estimation with only a minor increase in computational requirements. The algorithms are evaluated with respect to improving automatic recognition of speech in the presence of additive noise and shown to outperform other enhancement methods in this application. >

Analytical placement: A linear or a quadratic objective function?

Abstract: This paper addresses the problem of cell placement which is considered crucial for layout quality. Based on the combined analytical and partitioning strategy successfully applied in the GORDIAN placement tool, we discuss the consequences of using linear or quadratic objective functions. By joining the linear objective with an efficient quadratic programming approach, and by applying a refined iterative partitioning scheme, we obtain placements of excellent quality. The effect of a quadratic and a linear objective function on the chip area after final routing is demonstrated for benchmark circuits and other circuits with up to 21 000 cells.

Convergence estimates for product iterative methods with applications to domain decomposition

Abstract: In this paper, we consider iterative methods for the solution of symmetric positive definite problems on a space % which are defined in terms of products of operators defined with respect to a number of subspaces. The simplest algorithm of this sort has an error-reducing operator which is the product of orthogonal projections onto the complement of the subspaces. New normreduction estimates for these iterative techniques will be presented in an abstract setting. Applications are given for overlapping Schwarz algorithms with many subregions for finite element approximation of second-order elliptic problems.

Iterative procedures for reduction of blocking effects in transform image coding

Abstract: We propose a new iterative block reduction technique based on the theory of projection onto convex sets. The basic idea behind this technique 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. Since these components are missing in the original uncoded image, or at least can be guaranteed to be missing from the original image prior to coding, one step of our iterative procedure consists of projecting the coded image onto the set of signals which are bandlimited in the horizontal or vertical directions. Another constraint we have chosen in the restoration process has to do 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. Thus, in projecting the 'out of bound' transform coefficient onto this convex set, we will choose the upper (lower) bound of the quantization interval if its value is greater (less) than the upper (lower) bound. We present a few examples of our proposed approach.

A generalization of the Berlekamp-Massey algorithm for multisequence shift-register synthesis with applications to decoding cyclic codes

Abstract: A generalization of the Berlekamp-Massey algorithm is presented for synthesizing minimum length linear feedback shift registers for generating prescribed multiple sequences. A more general problem is first considered, that of finding the smallest initial set of linearly dependent columns in a matrix over an arbitrary field, which includes the multisequence problem as a special case. A simple iterative algorithm, the fundamental iterative algorithm (FIA), is presented for solving this problem. The generalized algorithm is then derived through a refinement of the FIA. Application of this generalized algorithm to decoding cyclic codes up to the Hartmann-Tzeng (HT) bound and Roos bound making use of multiple syndrome sequences is considered. Conditions for guaranteeing that the connection polynomial of the shortest linear feedback shift register obtained by the algorithm will be the error-locator polynomial are determined with respect to decoding up to the HT bound and special cases of the Roos bound. >

The multiple-call hand-off problem in high-capacity cellular communications systems

Abstract: The author presents a preliminary analytical model that characterizes the central issues of the hand-off problem when vehicles can support multiple calls simultaneously. In such cases a cell boundary crossing by a single vehicle can generate multiple hand-off attempts. A suitable vector state representation is identified which casts the problem as a multidimensional birth-death process. An iterative method is used to find implicit hand-off parameters for systems in statistical equilibrium. Theoretical performance characteristics that show blocking, hand-off failure, and forced termination probabilities as functions of communication traffic are determined. >

The four point explicit decoupled group (EDG) Method: a fast poisson solver

Abstract: The aim of this paper is to introduce a four point explicit decoupled group (EDG) iterative method as a new Poisson solver. The method is shown to be very much faster compared to existing explicit group (EG) methods due to D. J. Evans and M. J. Biggins (1982) and W. Yousif and D. J. Evans (1985). Some numerical experiments are included to confirm our recommendation.

Recovery of signals from nonuniform samples using iterative methods

Abstract: An iterative method to recover a bandlimited signal from its ideal nonuniform samples is proposed. The convergence of iterations is proved, and general regions for convergence are found. It is shown that the iterative method is also applicable to other forms of nonuniform sampling, i.e. natural sampling and interpolated sampling (such as sample-and-hold signal). Simulation results show that this method works effectively and fairly fast, and the errors after a few iterations are negligible if a particular sufficient condition is satisfied or the sampling rate is higher than the Nyquist rate. >

Expanding the range of convergence of the CORDIC algorithm

Abstract: The limitations on the numerical values of the functional arguments that are passed to the CORDIC computational units are discussed, with a special emphasis on the binary, fixed-point hardware implementation Research in the area of expanding the allowed ranges of the input variables for which accurate output values can be obtained is presented The methods proposed to expand the range of convergence for the CORDIC algorithm do not necessitate any unwidely overhead calculation, thus making this work amenable to a hardware implementation The number of extra iterations introduced in the modified CORDIC algorithms is significantly less than the number of extra iterations discussed elsewhere This reduction in the number of extra iterations will lead to a faster hardware implementation Examples demonstrate the usefulness of the methods in realistic situations >

Rational iterative methods for the matrix sign function

Abstract: In this paper an analysis of rational iterations for the matrix sign function is presented. This analysis is based on Pade approximations of a certain hypergeometric function and it is shown that l...

Numerical evaluation of iterative and noniterative methods for the solution of the nonlinear richards equation

Abstract: Several noniterative procedures for solving the nonlinear Richards equation are introduced and compared to the conventional Newton and Picard iteration methods. Noniterative strategies for the numerical solution of transient, nonlinear equations arise from explicit or linear time discretizations, or they can be obtained by linearizing an implicit differencing scheme. We present two first order accurate linearization methods, a second order accurate two-level “implicit factored” scheme, and a second order accurate three-level “Lees” method. The accuracy and computational efficiency of these four schemes and of the Newton and Picard methods are evaluated for a series of test problems simulating one-dimensional flow processes in unsaturated porous media. The results indicate that first order accurate schemes are inefficient compared to second order accurate methods; that second order accurate noniterative schemes can be quite competitive with the iterative Newton and Picard methods; and that the Newton scheme is no less efficient than the Picard method, and for strongly nonlinear problems can outperform the Picard scheme. The two second order accurate noniterative schemes appear to be attractive alternatives to the iterative methods, although there are concerns regarding the stability behavior of the three-level scheme which need to be resolved. We conclude that of the four noniterative strategies presented, the implicit factored scheme is the most promising, and we suggest improved formulations of the method.

Iterative Wiener filters for image restoration

Abstract: The iterative Wiener filter, which successively uses the Wiener-filtered signal as an improved prototype to update the covariance estimates, is investigated. The convergence properties of this iterative filter are analyzed. It has been shown that this iterative process converges to a signal which does not correspond to the minimum mean-squared-error solution. Based on the analysis, an alternate iterative filter is proposed to correct for the convergence error. The theoretical performance of the filter has been shown to give minimum mean-squared error. In practical implementation when there is unavoidable error in the covariance computation, the filter may still result in undesirable restoration. Its performance has been investigated and a number of experiments in a practical setting were conducted to demonstrate its effectiveness. >

A theoretical comparison of the Arnoldi and GMRES algorithms

Abstract: Two recently developed Krylov methods for solving linear systems are Arnoldi 's method and the Generalized Minimum Residual (GMRES) method The GMRES method has been considered superior to Arnoldi's method due in part to the fact that GMRES never breaks down in the way Arnoldi's algorithm can. However, it is shown that there is a relationship between breakdowns in the two methods. Specifically, it is shown that GMRES does exhibit breakdowns very similar to that of Arnoldi, often referred to as the “stagnation” of GMRES. A relationship between the norms of the residuals for Arnoldi and GMRES is also given which shows exactly how much larger the residual norm for Arnoldi is than that for GMRES. In general, the results in the paper suggest that if one of the methods performs poorly on a particular problem, then so will the other.

An iterative learning control of robot manipulators

Abstract: An iterative learning scheme comprising a unique feedforward learning controller and a linear feedback controller is presented. In the feedback loop, the fixed-gain PD controller provides a stable open neighborhood along a desired trajectory. In the feedforward path, on the other hand, a learning control strategy is exploited to predict the desired actuator torques. It is shown that the predicted actuator torque converges to the desired one as the iteration number increases. The convergence is established based on the Lyapunov stability theory. The proposed learning scheme is structurally simple and computationally efficient. Moreover, it possesses two major advantages: the ability to reject unknown deterministic disturbances and the ability to adapt itself to the unknown system parameters. >