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In this paper, two simplified versions of the belief propagation algorithm for fast iterative decoding of low-density parity check codes on the additive white Gaussian noise channel are proposed. Both versions are implemented with real additions only, which greatly simplifies the decoding complexity of belief propagation in which products of probabilities have to be computed. Also, these two algorithms do not require any knowledge about the channel characteristics. Both algorithms yield a good performance-complexity tradeoff and can be efficiently implemented in software as well as in hardware, with possibly quantized received values. Index Terms - APP decoding, belief propagation, block codes, four-density parity check codes, iterative decoding.

In this paper, a variant of the Newton method, which uses a fast solution of the direct problem and a dual mesh, is proposed. Computational and physical experiments with simple two-dimensional high-contrast phantoms are discussed, and a full-scaled image of a two-dimensional mathematical model of a human torso is obtained. Index Terms - Image reconstruction, inverse problems, iterative methods, microwave imaging, Newton method, tomography.

A nonlinear Poisson equation and an eigenvalue problem for Schrodinger's equation were used to develop a physical model describing quantum wire bound states. An iteration scheme was implemented through an expression of quantum electron density dependence on electrostatic potential. The iteration approach allowed the development of a solution for the two-dimensional Schrodinger-Poisson conditions in quantum structures.

Iterative simulation techniques are becoming standard tools in Bayesian statistics, a notable example being the Gibbs sampler, whose draws form a Markov chain. Standard practice is to run the simulation until convergence is approached in the sense of the draws appearing to be stationary. At this point, the set of stationary draws can be used to provide an estimate of the target distribution. However, when the distributions involved are normal and the draws form a Markov chain, the target distribution can be reliably estimated by maximum likelihood (ML) using draws before their convergence to the target distribution. This fact suggests that the normal-based ML estimates can be exploited to estimate the mean and covariance matrix of an approximately normal target distribution before convergence is reached, and that these estimates can be used to define a restarting distribution for the simulation. Here, we describe the needed technology and explore its relevance to practice. The tentative conclusion is that the Markov-Normal restarting procedure can be computationally advantageous when the target distribution is nearly normal, especially in massively parallel or distributed computing environments where many sequences can be run for the same effective cost as one sequence. Key words: EM algorithm; Gibbs sampler; Markov chain Monte Carlo; The multivariate t distribution; Time series

A look-ahead method for Value Iteration Algorithms used in solving both discounted and undiscounted Markov decision processes is presented. Based on the value-oriented concept which incorporates multiple adaptive relaxation factors, the approach leads to procedures which perform better than the separate application of either the concept of value oriented or of relaxation. The approach also appears useful in solving large-scale Markov decision processes.

The 'Modified Picard' Method Celia et al. (1990) developed 'A general mass-conservative numerical solution for the unsaturated flow equation,' applying what they cared the 'modified Picard' iteration method to the [...]

An iterative method for calculating the eigenvector derivatives involved in structural designing and planning is discussed. The accelerated subspace iteration method is able to present the parameters of a dynamic structural system in terms of simple numerical expressions that can be solved simultaneously using computer algorithm. A comparative study reveals that the accelerated subspace iteration approach is more reliable than conventional techniques in the speedy calculations of eigenvector derivatives.

David Adland and Arthur J. Caplan pointed out that the model proposed by Whitehead (2002) suffered from an incorrect interpretation of the shift coefficient and secondly, it omitted variables when covariates are included. Whitehead accepts their comments and presents a revised model inspired by Aadland and Caplan.

General software for preconditioning the iterative solution of linear systems is greatly lagging behind the literature. This is partly because specific problems need specific matrix and preconditioner data structures in […]