Abstract: The kinematic transformation between task space and joint configuration coordinates is nonlinear and configuration dependent. A solution to the inverse kinematics is a vector of joint configuration coordinates that corresponds to a set of task space coordinates. For a class of robots closed form solutions always exist, but constraints on joint displacements cannot be systematically incorporated in the process of obtaining a solution. An iterative solution is presented that is suitable for any class of robots having rotary or prismatic joints, with any arbitrary number of degrees of freedom, including both standard and kinematically redundant robots. The solution can be obtained subject to specified constraints and based on certain performance criteria. The solution is based on a new rapidly convergent constrained nonlinear optimization algorithm which uses a modified Newton-Raphson technique for solving a system nonlinear equations. The algorithm is illustrated using as an example a kinematically redundant robot.

Abstract: Iterative schemes for NMR have been developed by several groups. A theoretical framework based on mathematical dynamics is described for such iterative schemes in nonlinear NMR excitation. This is applicable to any system subjected to coherent radiation or other experimentally controllable external forces. The effect of the excitation, usually a pulse sequence, can be summarized by a propagator or superpropagator (U). The iterative scheme (F) is regarded as a map of propagator space into itself, U n+1=F U n . One designs maps for which a particular propagator U or set of propagators {U} is a fixed point or invariant set. The stability of the fixed points along various directions is characterized by linearizing F around the fixed point, in analogy to the evaluation of an average Hamiltonian. Stable directions of fixed points typically give rise to broadband behavior (in parameters such as frequency, rf amplitude, or coupling constants) and unstable directions to narrowband behavior. The dynamics of the maps are illustrated by ‘‘basin images’’ which depict the convergence of points in propagator space to the stable fixed points. The basin images facilitate the optimal selection of initial pulse sequences to ensure convergence to a desired excitation. Extensions to iterative schemes with several fixed points are discussed. Maps are shown for the propagator space S O(3) appropriate to iterative schemes for isolated spins or two‐level systems. Some maps exhibit smooth, continuous dynamics whereas others have basin images with complex and fractal structures. The theory is applied to iterative schemes for broadband and narrowband π (population inversion) and π/2 rotations, MLEV and Waugh spin decoupling sequences, selective n‐quantum pumping, and bistable excitation.

Abstract: In this paper, the Alternating Group Explicit (AGE) method is developed and applied to derive the solution of a 2 point boundary value problem. The analysis clearly shows the method to be analogous to the A.D.I. method. The extension of the method to ultidimensional problems and techniques for improving the convergence rate and attaining higher order accuracy are also given.

Abstract: In the local basis-function approach, a reconstruction is represented as a linear expansion of basis functions, which are arranged on a rectangular grid and possess a local region of support. The basis functions considered here are positive and may overlap. It is found that basis functions based on cubic B-splines offer significant improvements in the calculational accuracy that can be achieved with iterative tomographic reconstruction algorithms. By employing repetitive basis functions, the computational effort involved in these algorithms can be minimized through the use of tabulated values for the line or strip integrals over a single-basis function. The local nature of the basis functions reduces the difficulties associated with applying local constraints on reconstruction values, such as upper and lower limits. Since a reconstruction is specified everywhere by a set of coefficients, display of a coarsely represented image does not require an arbitrary choice of an interpolation function.

Abstract: In this paper we apply the so-called Hachtel's augmented matrix method for solving linear least squares problems to static state estimation. This method does not seem to have been applied in power system state estimation by others. The test system is the 99-bus main Norwegian grid. Hachtel's method is compared to two versions of the normal equations approach and is found to greatly improve numerical stability, which is important for ill-conditioned systems. It requires less computing time than the standard normal equations method, while needing somewhat more computer storage.

Abstract: The computational complexity of nonlinear adaptive noise cancellation can be reduced by restricting the nonlinearity expected in the reference path to the noise canceler. The class of zero memory nonlinearities preceded by linear processors in the reference path is considered. Noniterative and iterative methods of system identification are applied to the determination of processor parameters in the noise canceler. The computational requirements of each of the algorithms are compared, and the iterative method is modified for improved convergence. Experimental results are presented for the modified iterative algorithm.

Abstract: A practical design method is presented for three-dimensional transonic wings with prescribed pressure distributions. The method is based on an iterative "residual-correction" concept. The residual, defined as the difference between the computed and the prescribed pressure distributions at each iteration step, is determined by the use of an existing direct analysis code for a transonic wing with or without the body. The wing geometry correction to compensate for the residual can be approximately obtained from the inverse solution code developed in the present study. The inverse (correction) problem is mathematically reduced to a Dirichlet boundary value problem that is solved here by the aid of the transonic integral equation method. Some of the design results are also presented for transonic swept wings.

Abstract: This paper examines iterative methods for solving the semiconductor device equations. The emphasis is on fully coupled methods, because of the failure of decoupled methods for on-state devices. Using the PISCES-II device simulator as a vehicle, incomplete factorization and operator decomposition iterative methods are presented for solving the Newton equations. The dependencies of these methods on factors such as choice of variables, bias condition and initial guess are analyzed. The results are compared with sparse Gaussian elimination.

Abstract: The standard approach to the solution of the weighted least square (WLS) state estimation in power system is the iterative normal equations method. Occasional ill-conditioning has been experienced with this method. Recently alternative solution approaches based on orthogonal transformations have been proposed. Sparsity generally suffers in these methods. In this paper, the network condition which causes ill- conditioning is studied. A hybrid approach which enjoys the same numerical robustness of the orthogonal methods with sparsity close to the standard WLS method is presented. The modification needed to implement the hybrid method on an existing standard WLS state estimation program is quite small.

Abstract: There is a new and direct servo-control method called "Learning Control" which has a good advantage that the command input is not necessary a function generated from time-invariant linear systems but is required in conventional servo-theory using "Internal Model Principle". Therefore, this new theory is very attractive since it may estabilish a new foundation of servo-theory in which the shape of the command is arbitrary. The idea is very simple, we determine the input function U(s) satisfying R(s)=G(s)U(s) using some iterative method. In this paper, we derive conditions on the convergence of this method and practical design procedures, and the results are applied to the trajectory control of robot arm such that the tip of the arm draws any shape with satisfactory precision in several trials.

Abstract: An analysis of the rate-distortion performance of differential pulse code modulation (DPCM) schemes operating on discrete-time auto-regressive processes is presented. The approach uses an iterative algorithm for the design of the predictive quantizer subject to an entropy constraint on the output sequence. At each stage the iterative algorithm optimizes the quantizer structure, given the probability distribution of the prediction error, while simultaneously updating the distribution of the resulting prediction error. Different orthogonal expansions specifically matched to the source are used to express the prediction error density. A complete description of the algorithm, including convergence and uniqueness properties, is given. Results are presented for rate-distortion performance of the optimum DPCM scheme for first-order Gauss-Markov and Laplace-Markov sources, including comparisons with the corresponding rate-distortion bounds. Furthermore, asymptotic formulas indicating the high-rate performance of these schemes are developed for both first-order Gaussian and Laplacian autoregressive sources.

Abstract: In two earlier papers [SIAM J. Numer. Anal., 19 (1982), pp. 924–929; 21 (1984), pp. 255–262], we developed an algebraic convergence theory for a class of multigrid methods applied to positive definite self-adjoint linear operator equations. The purpose of the present paper is to extend these results by eliminating an earlier approximation order restriction, developing additional rate estimates and allowing for very general relaxation schemes, including those that are nonstationary and nonsymmetric. These results apply to most well-known iterative methods and preconditioners.

Abstract: An iterative method is developed for the solution of the steady Euler equations for inviscid flow. The system of hyperbolic conservation laws is discretized by a finite-volume Osher-discretization. The iterative method is a multiple grid (FAS) iteration with symmetric Gauss-Seidel (SGS) as a relaxation method. Initial estimates are obtained by full multigrid (FMG). In the pointwise relaxation the equations are kept in block-coupled form and local linearization of the equations and the boundary conditions is considered. The efficient formulation of Osher's discretization of the 2-D non-isentropic steady Euler equations and its linearization is presented. The efficiency of FAS-SGS iteration is shown for a transonic model problem. It appears that, for the problem considered, the rate of convergence is almost independent of the gridsize and that for all meshsizes the discrete system is solved up to truncation error accuracy in only a few (2 or 3) iteration cycles.

Abstract: A new fully implicit formulation for compositional simulators is presented. Rather than solving for pressure, saturations and phase compositions, the new formulation solves for pressure, overall concentrations and K-values. This change of primary unknowns to be solved improves numerical stability by yielding a more diagonally dominant Jacobian. The use of K-values as primary unknowns also allows the composition constraints to be solved separately from the other equations. The solution of the constraint equations is very efficient because they can be reformulated as monotonic functions*. The primary unknowns are further classified into reduced-unknowns and pivotal-unknowns. The latters are eliminated from the mass conservation equations using the fugacity equalities and constraints. The pivotal-unknowns are selected according to the sensitivity of the equations to the unknowns. This selection conforms to the partial pivoting strategy of Gaussian elimination and enhances numerical stability. Finally, a partial solution method is introduced to eliminate unnecessary calculations of those equations which have met the convergence criteria. For a simple system, it is shown that the new formulation results in a more diagonally dominant Jacobian matrix. Numerical experiments involving one dimensional multicontact-miscibile (MCM) and immiscible problems, a two dimensional MCM problem and a three dimensional MCM problem are conductedmore » to illustrate the capability and efficiency of the new formulation. Results indicate that the number of iterations per time step required by the new formulation is only about 40% - 60% of an existing fully implicit scheme. It is almost as low as that required by an IMPES scheme.« less

Abstract: It is desired to preprocess an input image so that, when it is distorted by an imaging system, a prescribed output image is produced. The system of interest is a linear, shift-invariant, band-limited system followed by a hard limiter. Such a system is found, for example, in microphotography, when a camera that is band limited by diffraction effects is used to print on very-high-contrast film. In this paper, an iterative solution that employs alternating projections is presented. Two variations of the procedure, which is similar to the Gerchberg–Papoulis algorithm, are applied to several examples having different space–bandwidth products. Also, a method of overrelaxing the projections to improve convergence is studied.

Abstract: A study is conducted of the stability of mesh refinement in space and time for several different interface equations and finite-difference approximations. First, a root condition which implies stability for the initial-boundary value problem for this type of interface is derived. From the root condition, the stability of several interface equations is proved, using the maximum principle. In some cases, the final verification steps can be done analytically; in other cases, a simple computer program has been written to check the condition for values of a parameter along the boundary of the unit circle. Using this method, stability for Lax-Wendroff with all the interface conditions considered, and for Leapfrog with interpolation interface conditions when the fine and coarse grids overlap is proved.

Abstract: A synthetic method has been developed to accelerate the iterative convergence of the multigroup radiative diffusion equations with temporally implicit material-radiation coupling. The performance of the method is characterized by means of a Fourier analysis. Computational results are given and are found to be consistent with the analysis. Overall, the method appears to be quite effective.

Abstract: SUMMARY This note introduces certain stress smoothing procedures and the so called ‘Loubignac-Cantin’ iteration for restoration of momentum balance in the smoothed stress fields. It is shown that this iteration corresponds precisely to the solution of mixed formulations in which the stresses (or strains) and the displacements are used as primary variables. The procedure has a very wide field of application and promises to add considerable accuracy to f.e.m. results by a small additional expenditure. INTRODUCTION Displacement formulations of stress analysis problems (or equivalent flow problems) result, as is well known, in discontinuous and inaccurate stress fields. Various techniques of stress ‘averaging’ and ‘smoothing’ have been used since the advent of finite element methods, the most effective of these being based on a ‘projection’ techniq~el-~. In these we proceed as follows: First solve (using the notaton of Reference 4) the equilibrium statement k=Ku=f Second, compute stresses

Abstract: The unsteady form of the full potential equation is solved in conservation form by an implicit method based on approximate factorization. At each time level, internal Newton iterations are performed to achieve time accuracy and computational efficiency. A local time linearization procedure is introduced to provide a good initial guess for the Newton iteration. A novel flux-biasing technique is applied to generate proper forms of the artificial viscosity to treat hyperbolic regions with shocks and sonic lines present. The wake is properly modeled by accounting not only for jumps in phi, but also for jumps in higher derivatives of phi, obtained by imposing the density to be continuous across the wake. The far field is modeled using the Riemann invariants to simulate nonreflecting boundary conditions. The resulting unsteady method performs well which, even at low reduced frequency levels of 0.1 or less, requires fewer than 100 time steps per cycle at transonic Mach numbers. The code is fully vectorized for the CRAY-XMP and the VPS-32 computers.

Abstract: A method that combines internal state estimation and external network modeling is developed. The external system is represented by an unreduced load flow model. One state estimation covering both the internal system and the external system is used. The external system operating data on power injections and bus voltages are entered as pseudo-measurements. At each iteration the set of active pseudo- measurements are selected to conform with the specified variables in a load flow program. Because such a set of non-redundant measurements is used, the internal state estimation is not affected by the external system pseudo-measurements. External generation MVAR and controlled bus voltage limits are enforced. A technique is developed to make a pseudo-measurement dormant. Using the dormant-measurement technique, it is possible to maintain the same external system state estimation formulation while the PV-PQ switching takes place from iteration to iteration. The method can easily be implemented by modifying an existing state estimation program. It has been implemented in a fast model-decoupled estimation program. Because of the dormant measurement technique, the constant gain matrix evaluated at flat voltage is used in every iteration. The method has been tested on the IEEE 14- bus, 30-bus, and Brazilian 66-bus systems. Excellent results are obtained. The number of iterations for the method to converge is usually the same as the regular state estimation runs. Thus the method presented here achieves simultaneously the internal state estimation and the external network modeling without adversely affecting the internal state estimation.

Abstract: An efficient block overrelaxation algorithm is presented for the solution of the steady-state dam seepage problem. The formulation of Alt is used in conjunction with a finite element method on a fixed mesh to obtain a finite dimensional problem which is then solved by the algorithm. Some similarities of the formulation and the residual flow method of Desai are also discussed. Numerical results are compared with results of other authors.

Abstract: This paper introduces a general formulation of constrained iterative restoration algorithms in which deterministic and/or statistical information about the undistorted signal and statistical information about the noise are directly incorporated into the iterative procedure. This a priori information is incorporated into the restoration algorithm by what we call "soft" or statistical constraints. Their effect on the solution depends on the amount of noise on the data; that is, the constraint operator is "turned off" for noiseless data. The development of the new iterative algorithm is based on results from regularization techniques for stabilizing ill-posed problems.

Abstract: An extremly fast, simple, efficient and reliable economic dispatch algorithm is presented. The algorithm utilizes a closed form expression for the calculation of the Lambda, as well as taking care of total transmission loss changes due to generation change, thereby-avoiding any iterative processes in the calculations. The closed form expression presented for Lambda can be used with any type of incremental transmission loss calculation. For this algorithm, penalty factors are derived based upon the Newton's method. An efficient method to implement the algorithm in power control centers is discussed. The algorithm presented has excellent convergence properties.

Abstract: A new method is proposed for solving the problem of minimum-cost expansion of power transmission networks. The problem is formulated as a mixed-integer program that explicitly considers both the investment costs of new lines and the operating costs associated with the system. The d.c. load flow equations for the network are embedded in the constraints of the mathematical model to avoid sub-optimal solutions that can arise if the enforcement of such constraints is done in an indirect way. The solution of the model gives the best line additions, and also provides information regarding the optimum generation at each generation point. The security is attained by an iterative procedure using a concept similar to that of the Cutting Plane methods of integer programming. The "Security Cuts' successively exclude the insecure solutions from the solution space of the problem until the solution obtained by the cost minimizing algorithm is a secure one. The important feature of this procedure is that the added constraints never exclude any secure solutions, thus security is attained without losing optimality. It is shown that the model is applicable to both static and multi-stage planning cases, and an application of the method to a real-world example with 22 right-of-ways is given.

Abstract: A method for solving problems of the form is presented. The approach of Levenberg and Marquardt is used, except that the linear least squares subproblem arising at each iteration is not solved exactly, but only to within a certain tolerance. The method is most suited to problems in which the Jacobian matrix is sparse. Use is made of the iterative algorithm LSQR of Paige and Saunders for sparse linear least squares.A global convergence result can be proven, and under certain conditions it can be shown that the method converges quadratically when the sum of squares at the optimal point is zero.Numerical test results for problems of varying residual size are given.