Abstract: Iterative inversion methods have been unsuccessful at inverting seismic data obtained from complicated earth models (e.g. the Marmousi model), the primary difficulty being the presence of numerous local minima in the objective function. The presence of local minima at all scales in the seismic inversion problem prevent iterative methods of inversion from attaining a reasonable degree of convergence to the neighborhood of the global minimum. The multigrid method is a technique that improves the performance of iterative inversion by decomposing the problem by scale. At long scales there are fewer local minima and those that remain are further apart from each other. Thus, at long scales iterative methods can get closer to the neighborhood of the global minimum. We apply the multigrid method to a subsampled, low-frequency version of the Marmousi data set. Although issues of source estimation, source bandwidth, and noise are not treated, results show that iterative inversion methods perform much better when employed with a decomposition by scale. Furthermore, the method greatly reduces the computational burden of the inversion that will be of importance for 3-D extensions to the method.

Abstract: A new munerical method for computing non-Local Thermodynamic Equilibrium (non-LTE) model stellar atmospheres is presented. The method, called the hybird complete linearization/accelerated lambda iretation (CL/ALI) method, combines advantages of both its constituents. Its rate of convergence is virtually as high as for the standard CL method, while the computer time per iteration is almost as low as for the standard ALI method. The method is formulated as the standard complete lineariation, the only difference being that the radiation intensity at selected frequency points is not explicity linearized; instead, it is treated by means of the ALI approach. The scheme offers a wide spectrum of options, ranging from the full CL to the full ALI method. We deonstrate that the method works optimally if the majority of frequency points are treated in the ALI mode, while the radiation intensity at a few (typically two to 30) frequency points is explicity linearized. We show how this method can be applied to calculate metal line-blanketed non-LTE model atmospheres, by using the idea of 'superlevels' and 'superlines' introduced originally by Anderson (1989). We calculate several illustrative models taking into accont several tens of thosands of lines of Fe III to Fe IV and show that the hybrid CL/ALI method provides a robust method for calculating non-LTE line-blanketed model atmospheres for a wide range of stellar parameters. The results for individual stellar types will be presented in subsequent papers in this series.

Abstract: The fast multipole method (FMM) has been implemented to speed up the matrix-vector multiply when an iterative method is used to solve the combined field integral equation (CFIE). FMM reduces the complexity from O(N2) to O(N1.5). With a multilevel fast multipole algorithm (MLFMA), it is further reduced to O(N log N). A 110, 592-unknown problem can be solved within 24 h on a SUN Sparc 10. © 1995 John Wiley & Sons, Inc.

Abstract: A new mixed finite element method for computing viscoelastic flows is presented. The mixed formulation is based on the introduction of the rate of deformation tensor as an additional unknown. Contrary to the popular EVSS method [D. Rajagopalan, R.A. Brown and R.C. Armstrong, J. Non-Newtonian Fluid Mech., 36 (1990) 159], no change of variable is performed into the constitutive equation. Hence, the described method can be used to compute solutions of rheological models where the EVSS method does not apply. The numerical strategy uses a decoupled iterative scheme as a preconditioner for the GMRES algorithm. The stability and the robustness of the method are investigated on two benchmark problems: the 4:1 contraction flow problem and the stick-slip flow problem. Numerical results for the PTT [N. Phan-Thien and R.I. Tanner, J. Non-Newtonian Fluid Mech., 2 (1977) 353] and the Grmela [J. Grmela, J. Rheology, 33 (1989) 207] models show that our method is remarkably stable and cheap in computer time and memory.

Abstract: We propose a significantly improved space mapping (SM) strategy for electromagnetic (EM) optimization. Instead of waiting for upfront EM analyses at several base points, our new approach aggressively exploits every available EM analysis, producing dramatic results right from the first step. We establish a relationship between the novel SM optimization and the quasi-Newton iteration for solving a system of nonlinear equations. Approximations to the matrix of first-order derivatives are updated by the classic Broyden formula. A high-temperature superconducting microstrip filter design solution emerges after only six EM simulations with sparse frequency sweeps. Furthermore, less CPU effort is required to optimize the filter than is required by one single detailed frequency sweep. We also extend the SM concept to the parameter extraction phase, overcoming severely misaligned responses induced by inadequate empirical models. This novel concept should have a significant impact on parameter extraction of devices.

Abstract: A procedure is presented for efficient generation of high-quality two- or three-dimensional unstructured grids of triangular or tetrahedral elements. The present procedure uses an iterative point creation and insertion scheme wherein points are created using advancing-front type point placement. Initially, the connectivity for these generated points is obtained by directly subdividing the elements which contain them, without regard to quality. This connectivity is then improved by iteratively using local reconnection subject to a quality criterion. For two dimensions, a min-max criterion is used and for three dimensions, a Delaunay in-sphere criterion followed by a min-max type criterion is used. The overall procedure is applied repetitively until a complete field grid is generated with a desired point distribution. Grid quality and performance statistics are presented for a variety of two- and three-dimensional configurations. The combined quality and efficiency attributes of this procedure appear to be a substantial improvement over existing methods.

Abstract: Recently, a bilevel programming approach has been used for estimation of origin-destination (O-D) matrix in congested networks This approach integrates the conventional generalized least squares estimation model and the standard network equilibrium model into one process We extend this approach and develop a more general model and efficient heuristic algorithms to handle more realistic situation where link flow interaction cannot be ignored The extended model is formulated in the form of a bilevel programming problem with variational inequality constraints The upper-level problem seeks to minimize the sum of error measurements in traffic counts and O-D matrices, while the lower-level problem represents a network equilibrium problem formulated as variational inequalities, which guarantees that the estimated O-D matrix and corresponding link flows satisfy the network equilibrium conditions Two computational techniques are presented for solving the bilevel O-D matrix estimation model One is a heuristic iterative algorithm between traffic assignment and O-D matrix estimation and the other one is a sensitivity analysis based heuristic algorithm Properties of the two algorithms are analyzed theoretically and compared numerically with small network examples It is concluded that both algorithms can be used as efficient approaches for the bilevel O-D matrix estimation problems

Abstract: A new heuristic algorithm is presented for constructing minimum-cost multicast trees with delay constraints. The new algorithm can set variable delay bounds on destinations and handles two variants of the network cost optimization goal: one minimizing the total cost (total bandwidth utilization) of the tree, and another minimizing the maximal link cost (the most congested link). Instead of the single-pass tree construction approach used in most previous heuristics, the new algorithm is based on a feasible search optimization method which starts with the minimum-delay tree and monotonically decreases the cost by iterative improvement of the delay-bounded tree. The optimality of the costs of the delay-bounded trees obtained with the new algorithm is analyzed by simulation. Depending on how tight the delay bounds are, the costs of the multicast trees obtained with the new algorithm are shown to be very close to the costs of the trees obtained by the Kou, Markowsky and Berman's algorithm (1981).

Abstract: Part 1 Unstable problems: base formulations of problems ill-posed problems examples and its stability analysis the classification of methods for unstable problems with a priori information. Part 2 Iterative methods for approximation of fixed points and their application to ill-posed problems: basic classes of mappings convergence theorems for iterative processes iterations with correcting multipliers applications to problems of mathematical programming regularizing properties of iterations iterative processes with averaging iterative regularization of variation inequalities and of operator equations with monotone operators iterative regularization of operator equations in the partially-ordered spaces iterative schemes based on the Gauss-Newton method. Part 3 Regularization methods for symmetric spectral problems: L-basis of linear operator kernel analogies of Tikhonov's and Lavent'ev's methods the variational residual method and the quasisolutions method regularization of generalized spectral problem. Part 4 The finite-moment problem and systems of operators equations: statement of the problem and convergence of finite-dimensional approximations iterative methods on the basis of projections the Fejer processes with correcting multipliers FMP regularization in Hilbert spaces with reproducing kernels iterative approximation of solution of linear operator equation system. Part 5 Discrete approximation of regularizing algorithms: discrete convergence of elements and operators convergence of discrete approximations for Tikhonov's regularizing algorithm applications to integral and operator equations interpolation of discrete approximate solutions by splines discrete approximation of reconstuction of linear operator kernel basis finite-dimensional approximation of regularized algorithms on discontinuous functions classes. Part 6 Numerical applications: iterative algorithms for solving gravimetry problem computing schemes for finite-moment problem methods for experiment data processing in structure investigations of amorphous alloys. Appendix: correction parameters methods for solving integral equations of the first kind.

Abstract: A formulation based on the high frequency asymptotic principles of physical optics is developed for analyzing the scattering by relatively arbitrary open-ended waveguide cavities containing complex interior terminations. A magnetic field integral equation (MFIE) is obtained for the equivalent currents on the interior cavity walls and is solved using an iterative physical optics (IPO) algorithm which iteratively applies physical optics to account for multiple reflections inside the cavity. The number of iterations required for convergence is related to the expected number of important reflections. The IPO method is more approximate than a matrix solution of the MFIE, but it is quite accurate for electrically large cavities and is much more efficient. Numerical results are presented which demonstrate the convergence and accuracy of the method by comparison with modal reference solutions. >

Abstract: A new iterative approach to the solution of the Boltzmann equation is presented. The convergence of the iteration procedure is checked in reference to an isotropic solid subjected to a thermal gradient. The resulting thermal conductivity for an argon cyrstal at 80 K is consistent with the answer of a variational calculation previously performed in the frame of the same model. The extension of the method to any kind of transport problems, for any system of interacting particles, is suggested.

Abstract: As a means to obtain a more accurate description of traffic flows than that provided by the basic model of traffic assignment, there have been suggestions to impose upper bounds on the link flows. This can be done either by introducing explicit link capacities or by employing travel time functions with asymptotes at the upper bounds. Although the latter alternative has the disadvantage of inherent numerical ill-conditioning, the capacitated assignment model has been studied and applied to a limited extent, the main reason being that the solutions can not be characterized by the classical Wardrop equilibrium conditions; they may, however, be characterized as Wardrop equilibria in terms of a well-defined, natural generalized travel cost. The introduction of link capacity side constraints makes the problem computationally more demanding. The availability of efficient algorithms for the basic model of traffic assignment motivates the use of dualization approaches for handling the capacity constraints. We propose and evaluate an augmented Lagrangean dual method in which the uncapacitated traffic assignment subproblems are solved with the disaggregate simplicial decomposition algorithm. This algorithm fully exploits the subproblem's structure and has very favourable reoptimization capabilities; both these properties are necessary for achieving computational efficiency in iterative dualization schemes. The dual method exhibits a linear rate of convergence under a standard nondegeneracy assumption. The efficiency of the overall algorithm is demonstrated through experiments with capacitated versions of well-known test problems, with the conclusion that the introduction of link capacities increases the computing times with no more than a factor of four. The introduction of capacities and the algorithm suggested can be used to derive tolls for the reduction of flows on overloaded links. The solution strategy can be applied also to other types of traffic assignment models where side constraints have been added in order to refine a descriptive or prescriptive assignment model.

Abstract: This paper presents a receiving scheme intended to combat the detrimental effects of intersymbol interference for digital transmissions protected by convolutional codes. The receiver performs two successive soft-output decisions, achieved by a symbol detector and a channel decoder, through an iterative process. At each iteration, extrinsic information is extracted from the detection and decoding steps and is then used at the next iteration as in turbo-decoding. From the implementation point of view, the receiver can be structured in a modular way and its performance, in bit error rate terms, is directly related to the number of modules used. Simulation results are presented for transmissions on Gauss and Rayleigh channels. The results obtained show that turbo-equalization manages to overcome multipath effects, totally on Gauss channels, and partially but still satisfactorily on Rayleigh channels.

Abstract: The basic principles of an efficient new methodology for the calculation of the nonsinusoidal periodic steady state in power systems with nonlinear and time-varying components are described. All linear parts, including the network and part of the loads, are represented in the frequency domain, while nonlinear and time-varying components, mainly loads, are represented in the time domain. This hybrid process is iterative, with periodic, nonsinusoidal, bus voltages as inputs for both frequency domain solutions and time domain simulations: a current mismatch is calculated at each bus and used to update the voltages until convergence is reached. Thus the process, but not the solution, is decoupled for the individual harmonics. Its efficiency is enhanced by the use of Newton type algorithms for fast convergence to the periodic steady state in the time domain simulations. Potential applications of this methodology are in the computation of harmonic power flow and in the steady state initialization needed in the calculation of electromagnetic transients. >

Abstract: We propose a method for the solution of linear systems $AX = B$ where A is a large, possibly sparse, nonsymmetric matrix of order n, and B is an arbitrary rectangular matrix of order $n \times s$ with s of moderate size. The method uses a single Krylov subspace per step as a generator of approximations, a projection process, and a Richardson acceleration technique. It thus combines the advantages of recent hybrid methods with those for solving symmetric systems with multiple right-hand sides. Numerical experiments indicate that in several cases the method has better practical performance and significantly lower memory requirements than block versions of nonsymmetric solvers and other proposed methods for the solution of systems with multiple right-hand sides.

Abstract: Gaussian-elimination based shooting-Newton methods, a commonly used approach for computing steady-state solutions, grow in computational complexity like N/sup 3/, where N is the number of circuit equations. Just using iterative methods to solve the shooting-Newton equations results in an algorithm which is still order N/sup 2/ because of the cost of calculating the dense sensitivity matrix. Below, a matrix-free Krylov-subspace approach is presented, and the method is shown to reduce shooting-Newton computational complexity to that of ordinary transient analysis. Results from several examples are given to demonstrate that the matrix-free approach is more than ten times faster than using iterative methods alone for circuits with as few as 400 equations.

Abstract: In this paper, we present a tutorial report of the literature on the damped-least squares method which has been used for computing velocity inverse kinematics of robotic manipulators. This is a local optimization method that can prevent infeasible joint velocities near singular configurations by using a damping factor to control the norm of the joint velocity vector. However, the exactness of the inverse kinematic solution has to be sacrificed in order to achieve feasibility. The damping factor is an important parameter in this technique since it determines the trade-off between the accuracy and feasibility of the inverse kinematic solution. Various methods that have been proposed to compute an appropriate damping factor are described. Redundant manipulators, possessing extra degrees of freedom, afford more choice of inverse kinematic solutions than do non-redundant ones. The damped least-squares method has been used in conjunction with redundancy resolution schemes to compute feasible joint velocities for redundant arms while performing an additional subtask. We outline the different techniques that have been proposed to achieve this objective. In addition, we introduce an iterative method to compute the optimal damping factor for one of the redundancy resolution techniques.

Abstract: Multiple sequence alignment is an important problem in the biosciences. To date, most multiple alignment systems have employed a tree-based algorithm, which combines the results of two-way dynamic programming in a tree-like order of sequence similarity. The alignment quality is not, however, high enough when the sequence similarity is low. Once an error occurs in the alignment process, that error can never be corrected. Recently, an effective new class of algorithms has been developed. These algorithms iteratively apply dynamic programming to partially aligned sequences to improve their alignment quality. The iteration corrects any errors that may have occurred in the alignment process. Such an iterative strategy requires heuristic search methods to solve practical alignment problems. Incorporating such methods yields various iterative algorithms. This paper reports our comprehensive comparison of iterative algorithms. We proved that performance improves remarkably when using a tree-based iterative method, which iteratively refines an alignment whenever two subalignments are merged in a tree-based way. We propose a tree-dependent, restricted partitioning technique to efficiently reduce the execution time of iterative algorithms.

Abstract: This paper addresses the problem of optimizing a function over a finite or countably infinite set of alternatives, in situations where this objective function cannot be evaluated exactly, but has to be estimated or measured. A special focus is on situations where simulation is used to evaluate the objective function. We present two versions of a new iterative method for solving such discrete stochastic optimization problems. In each iteration of the proposed method, a neighbor of the “current” alternative is selected, and estimates of the objective function evaluated at the current and neighboring alternatives are compared. The alternative that has a better observed function value becomes the next current alternative. We show how one version of the proposed method can be used to solve discrete optimization problems where the objective function is evaluated using transient or steady-state simulation, and we show how the other version can be applied to solve a special class of discrete stochastic optimizati...

Abstract: This paper describes the steady-state analysis of self-excited induction generators (SEIG) using an iterative method. By considering the conductances connected across the air gap nodes, an iteration procedure is developed for the determination of the self-excited per-unit frequency, which enables the equivalent circuit to be completely solved. The proposed method involves only simple algebraic calculations, but the accuracy is good and convergence is rapid. The method is subsequently extended to include core loss effects and the analysis of SEIG with series capacitance compensation. Very good agreement between experimental and computed results has been obtained on a 2 kW laboratory machine. >

Abstract: Based on the least mean squares (LMS) algorithm, the LMS spectrum analyzer can be used to recursively calculate the discrete Fourier transform (DFT) of a sliding window of data. In this paper, we compare the LMS spectrum analyzer with the straightforward nonadaptive implementation of the recursive DFT. In particular, we demonstrate the robustness of the LMS spectrum analyzer to the propagation of roundoff errors, a property that is not shared by other recursive DFT algorithms. >

Abstract: In this paper an iterative finite element procedure is presented for the analysis of twoand three-dimensional piezoelectric continua. The procedure is applied to the steady-state analysis of two-di...

Abstract: The numerical analysis of various modeling formalisms profits from a structured representation for the generator matrix Q of the underlying continuous-time Markov chain, where Q is described by a sum of tensor (Kronecker) products of much smaller matrices. In this paper, we describe such a representation for the class of superposed generalized stochastic Petri nets (GSPNs), which is less restrictive than in previous work. Furthermore a new iterative analysis algorithm is proposed. It pays special attention to a memory-efficient representation of iteration vectors as well as to a memory-efficient structured representation of Q in consequence the new algorithm is able to solve models which have state spaces with several million states, where other exact numerical methods become impracticable on a common workstation.