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. >

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. >

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. >

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. >

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. >

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. >

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. >

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.

Abstract: We present a class of iterative methods for solving the problem of blind deconvolution of an unknown possibly non-minimum phase linear system driven by an unobserved input process. The methods converge monotonically at a very fast super-exponential rate to the desired solution in which the inverse of the unknown system is identified, and the input process is recovered up to a delay and possibly a constant phase shift. The proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the input process, provided that it is non-Gaussian.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

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. >

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...

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.

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. >

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. >

Abstract: A transformational approach aimed at improving the resource utilization in high level synthesis is introduced. The current implementation combines retiming and associativity in a single framework. This combination of transformations results in considerable area improvements, as is amply demonstrated by benchmark examples. A novel learning while searching iterative improvement probabilistic algorithm has been developed and is used to resolve the associated NP-complete combinatorial optimization problem. The effectiveness of the proposed algorithms and the transformations is demonstrated using standard benchmark examples, with the aid of statistical analysis, and through a comparison with estimated minimal bounds. The proposed algorithm has proven to be very effective in reaching the optimal solution as well as in runtime. >

Abstract: Nonlinear function approximation is often solved by finding a set of coefficients for a finite number of fixed nonlinear basis functions. However, if the input data are drawn from a high-dimensional space, the number of required basis functions grows exponentially with dimension, leading many to suggest the use of adaptive nonlinear basis functions whose parameters can be determined by iterative methods. The author proposes a technique based on the idea that for most of the data, only a few dimensions of the input may be necessary to compute the desired output function. Additional input dimensions are incorporated only where needed. The learning procedure grows a tree whose structure depends upon the input data and the function to be approximated. This technique has a fast learning algorithm with no local minima once the network shape is fixed, and it can be used to reduce the number of required measurements in situations where there is a cost associated with sensing. Three examples are given: controlling the dynamics of a simulated planar two-joint robot arm, predicting the dynamics of the chaotic Mackey-Glass equation, and predicting pixel values in real images from pixel values above and to the left. >

Abstract: An iterative reconstruction method which minimizes the effects of ill-conditioning is discussed. Based on the modified Newton-Raphson algorithm, a regularization method which integrates prior information into the image reconstruction was developed. This improves the conditioning of the information matrix in the modified Newton-Raphson algorithm. Optimal current patterns were used to obtain voltages with maximal signal-to-noise ratio (SNR). A complete finite element model (FEM) was used for both the internal and the boundary electric fields. Reconstructed images from phantom data show that the use of regularization optimal current patterns, and a complete FEM model improves image accuracy. The authors also investigated factors affecting the image quality of the iterative algorithm such as the initial guess, image iteration, and optimal current updating. >

Abstract: An algorithm is developed to define, from the data samples themselves, a frequency-weighted norm to use in minimum-weighted-norm extrapolation. The iterative procedure developed consists of using a periodogram spectrum estimate obtained from some samples of the signal estimate/extrapolation found at one iteration to define the weight that is used to estimate at the next iteration. This algorithm usually converges in less than 10 iterations to an extrapolation which is characterized as a nonparametric frequency-stationary extension of the data. The frequency resolution and extrapolation length are controlled by the length of a time-domain window used to obtain smooth spectral estimates between iterations. Examples are provided to illustrate the use of the algorithm for interpolation/extrapolation. The examples give comparable results to nonadaptive extrapolation methods without the need for a priori knowledge. For a certain spectral estimation example, the algorithm provides comparable resolution to the parametric methods with more accurate values of the relative strengths of the narrowband components. >

Abstract: This paper examines diagonally implicit iteration methods for solving implicit Runge–Kutta methods with high stage order on parallel computers. These iteration methods are such that after a finite number of m iterations, the iterated Runge–Kutta method belongs to the class of diagonally implicit Runge–Kutta methods (DIRK methods) using $mk$ implicit stages where k is the number of stages of the generating implicit Runge–Kutta method (corrector method). However, a large number of the stages of this DIRK method can be computed in parallel, so that the number of stages that have to be computed sequentially is only m. The iteration parameters of the method are tuned in such a way that fast convergence to the stability characteristics of the corrector method is achieved. By means of numerical experiments it is also shown that the solution produced by the resulting iteration method converges rapidly to the corrector solution so that both stability and accuracy characteristics are comparable with those of the corrector. This implies that the reduced accuracy often shown when integrating stiff problems by means of DIRK methods already available in the literature (which is caused by a low stage order) is not shown by the DIRK methods developed in this paper, provided that the corrector method has a sufficiently high stage order.

Abstract: An efficient algorithm, RITUAL (residual iterative technique for updating all Lagrange multipliers), for obtaining a placement of cell-based ICs subject to performance constraints is described. Using sophisticated mathematical techniques, one is able to solve large problems quickly and effectively. The algorithm is very simple and elegant, making it easy to implement. In addition, it yields very good results, as is shown on a set of real examples. The algorithm was tested on the ISCAS set of logic benchmark examples using parameters for 1 mu m CMOS technology. On average , there is a 25% improvement in the wire delay for these examples compared to TimberWolf-5.6 with a small impact on the chip area. >

Abstract: We investigate iterative methods for solving consistent linear systems arising from the kinetic theory of gases and for providing multicomponent diffusion coefficients for gaseous mixtures. Various iterative schemes are proved to be convergent by using the properties of matrices with convergent powers and the properties of nonnegative matrices. In particular, we investigate Stefan-Maxwell diffusion equations and we express the multicomponent diffusion matrix as a symmetric convergent series. We also rigorously justify the accuracy of Hirschfelder-Curtiss approximations with mass correctors often used to approximate diffusion velocities in gas mixtures.

Abstract: Extracting surface orientation and surface depth from a shaded image is one of the classic problems in computer vision. Many previous algorithms either violate integrability, i.e., the surface normals do not correspond to a feasible surface, or use regularization, which biases the solution away from the true answer. A recent iterative algorithm proposed by Horn overcomes both of these limitations but converges slowly. This paper uses a new algorithm, hierarchical basis conjugate gradient descent, to provide a faster solution to the shape from shading problem. This approach is similar to the multigrid techniques that have previously been used to speed convergence, but it does not require heuristic approximations to the true irradiance equation. The paper compares the accuracy and the convergence rates of the new techniques to previous algorithms.

Abstract: Various iterative deconvolution algorithms are evaluated that are commonly used to restore degraded chromatographic or spectroscopic peak data. The evaluation criteria include RMS errors, relative errors in peak areas, peak area variances, and rate of convergence. The iterative algorithms to be evaluated include Van Cittert's method, Van Cittert's method with constraint operators, relaxation based methods, and Gold's ratio method. The discussion also includes some enhancements that will improve the algorithms' convergence properties. >

Abstract: A number of iterative algorithms to solve integral equations arising in field problems are discussed. We describe the essential features of the Neumann Series, overrelaxation methods, Krylov subspace methods, and the conjugate gradient technique. Proofs of convergence of the conjugate gradient method are directly available when the underlying integral operator is self-adjoint, and in this case the method is equivalent to the Krylov method. However, for non-self-adjoint operators the conjugate gradient method requires an implicit symmetrization which results in poorer convergence than that obtained using the Krylov method. Some convergence results are also available for overrelaxation methods for both self-adjoint and non-self-adjoint operators. Relations between all of the methods will be described and numerical performance will be contrasted using a uniform square error criterion. All the methods are treated in the continuous operator form which is especially useful in using the physical setting to arrive at effective preconditioners.

Abstract: Methods for joint ocean-channel estimation and data recovery are derived using an optimal, maximum likelihood (ML) estimation criterion. The resulting ML problems may be complex, thus iterative algorithms are used, e.g. the expectation-maximization (EM) algorithm. The different methods correspond to different assumptions about the ocean channel. The theoretical derivation of these methods as well as preliminary results on simulated ocean data experiments are presented. >