A new iterative method for the analysis of longitudinally invariantwaveguide couplers

In this paper, a new iterative method to solve for the modal indices and field profiles of the supermodes of multichannel waveguide structures is proposed. This method combines the shift inverse power method with the simultaneous iteration method, and can be applied to any longitudinally invariant waveguide couplers problem very efficiently. Using this method, the characteristics of the leading supermodes can be obtained simultaneously. The validity and accuracy of this method are assessed by comparing to other existing methods for symmetric two-channel waveguide couplers. Results are in good agreement. Asymmetric two-channel and symmetric three-channel waveguide couplers are then considered to show the usefulness and versatility of the proposed method     

A robust iterative method for Born inversion

We present a robust iterative method to solve the inverse scattering problem in cases where the Born approximation is valid. We formulate this linearized inverse problem in terms of the unknown material contrast and the unknown contrast sources and we solve the problem by minimizing a cost functional consisting of two terms. The first term represents the differences between the actual data and the modeled data, while the second term represents the misfit in the constitutive relations between the contrast sources and the incident fields. In each iteration, the contrast sources and the contrast are reconstructed alternatingly, using subsequently a conjugate gradient step for the contrast source updates and a direct inversion of a diagonal matrix for the contrast. A further regularization with a multiplicative regularization factor is discussed. In this regularization procedure the relative variation of the contrast is minimized as well. As a test case we consider the two-dimensional (2-D) transverse magnetic polarization problem. Synthetic numerical examples are presented in order to compare the presented algorithm to the traditional Born algorithm. Results with respect to the inversion of experimental data are presented as well. In addition, some inversion results for the subsurface sensing problem, both in two and three dimensions, are presented.     

Preconditioning methods for improved convergence rates in iterative reconstructions

Because of the characteristics of the tomographic inversion problem, iterative reconstruction techniques often suffer from poor convergence rates-especially at high spatial frequencies. By using preconditioning methods, the convergence properties of most iterative methods can be greatly enhanced without changing their ultimate solution. To increase reconstruction speed, spatially invariant preconditioning filters that can be designed using the tomographic system response and implemented using 2-D frequency-domain filtering techniques have been applied. In a sample application, reconstructions from noiseless, simulated projection data, were performed using preconditioned and conventional steepest-descent algorithms. The preconditioned methods demonstrated residuals that were up to a factor of 30 lower than the assisted algorithms at the same iteration. Applications of these methods to regularized reconstructions from projection data containing Poisson noise showed similar, although not as dramatic, behavior.     

Improved convergence of iterative scheme for analysing arrays of finite size

The currents induced in a finite array of dipoles have been computed using an efficient iterative technique. A minimisation process is introduced which requires fewer iterations to obtain convergence. The currents obtained are compared with a method of moments solution applied to the same array.<>     

Improved convergence of numerical device simulation iterative algorithms

Two techniques are described which serve to minimize the problem of slow Newton convergence and, at times, divergence sometimes experienced in applying this iterative technique to the solution of nonlinear semiconductor equations. The truncated correction method limits the wide excursions in the solution parameters which can occur during the Newton iterative procedure and thereby permits fewer voltage increments to be used in applying large bias voltages (1000 V)in simulating semiconductor power device operation. The doping-incrementation method uses the technique of gradually incrementing the doping levels in the heavily doped regions in a device structure to provide better solution first guesses in the simulation of devices containing such regions. Substantial savings in computer time are obtained in applying these two numerical procedures.     

A new iterative bidirectional beam propagation method

A new bidirectional beam propagation method is developed for numerical simulation of wave-guiding structures with multiple longitudinal reflecting interfaces. It is an iterative method that works on the wave field components directly. Operator rational approximations developed in the one-way beam propagation method are used together with a modern Krylov subspace iterative method. Compared with earlier bidirectional beam propagation methods based on the transfer matrix formulation, the new method is numerically stable and models evanescent modes better     

An iterative method for solving scattering problems

An iterative method is developed for computing the current induced by plane wave excitation on conducting bodies of arbitrary shape. In this method, the scattering body is divided into lit- and shadow-side regions separated by the geometric optics boundary. The induced current at any point on the surface of the scatterer is expressed as the sum of an approximate optics current and a correction current. Both of these currents are computed by iteration for the lit and shadow regions separately. The general theory is presented and applied to the problems of scattering from a two-dimensional cylinder of circular and square cross sections. The results are compared with the method of moments and good agreement is obtained. This method does not give erroneous results at internal resonances of the scatterer, does not suffer from computer storage problems and can be extended to nonperfect conductors as well as to three-dimensional bodies.     

Discrete constrained iterative deconvolution algorithms with optimized rate of convergence

In this paper, some new constrained discrete deconvolution algorithms based on an iterative equation are presented. The constraints are—the signal extent (signal support)—the positivity—the level bounds. The algorithms minimize either the error energy or a positive functional. The connections with previous works are studied. An experimental comparison of the algorithms convergence speed is studied with a synthetic sequence to be recovered. The restoration error and both the deconvoluted signal and its spectrum show clearly the performances of the algorithms and their ability to achieve a spectral extrapolation. The deconvolution from noisy data is investigated.     

An iterative method for solving electrostatic problems

The method of steepest descent is applied to the solution of electrostatic problems. The relation between this method and the Rayleigh-Ritz, Galerkin's, and the method of least squares is outlined. Also, explicit error formulas are given for the rate of convergence for this method. It is shown that this method is also suitable for solving singular operator equations. In that case this method monotonically converges to the solution with minimum norm. Finally, it is shown that the technique yields as a by-product the smallest eigenvalue of the operator in the finite dimensional space in which the problem is solved. Numerical results are presented only for the electrostatic case to illustrate the validity of this procedure which show excellent agreement with other available data.     

A method toward improved convergence of moment-method solutions

A technique for improving the convergence of moment-method solutions through the use of a priori knowledge is presented. The idea is that known good approximations such as physical-optics current may be subtracted from the unknown total current with the result that the residual difference current, which is now the quantity to be determined, will converge more rapidly. Use of this method as applied to plane-wave scattering from conducting strips is given as an example.     

Fast convergence method for Lloyd-Max quantiser design

In Max quantiser design, a numerical method is usually employed to solve the Lloyd-Max equations. Poor accuracy and slow convergence rate are observed in most of the algorithms used. A fast convergence method is proposed here to generate the Max quantiser with minimum mean-square error. This is achieved by changing the integration limits and using a bisection method in solving the Lloyd-Max equations.     

An iterative current-based hybrid method for complex structures

This paper presents a general unified hybrid method for radiation and scattering problems such as antennas mounted on a large platform. The method uses a coupled electric-field integral equation (EFIE) and magnetic-field integral equation (MFIE) formulation, referred to as the hybrid EFIE-MFIE (HEM), in which the EFIE and MFIE are applied to geometrically distinct regions of an object. The HEM is capable of modeling arbitrary three-dimensional (3-D) metallic structures, including wires and both open and closed surfaces. We show that current-based hybrid techniques that utilize physical optics (PO) are an approximation of the HEM formulation. A numerical solution procedure is given that combines the moment method (EFIE) with an iterative Neumann series technique (MFIE). This permits one to effectively utilize the PO approximation when appropriate, and provides a general and systematic mechanism to correct the errors introduced by PO. Consequently, the HEM overcomes the inherent limitations of hybrid techniques which rely upon ansatz-based improvements of PO. The method is applied to the problem of radiation from objects that can be modeled using wires and metallic surfaces as fundamental elements. A representative example is given to demonstrate that the method can handle the difficult problem of a parasitic monopole located in the deep shadow region     

Efficient iterative design method for cosine-modulated QMF banks

An iterative algorithm for the design of multichannel cosine-modulated quadrature mirror-image filter (QMF) banks with near-perfect reconstruction is proposed. The objective function is formulated as a quadratic function in each step whose minimum point can be obtained using a closed-form solution. This approach has high design efficiency and leads to filter banks with high stopband attenuation and low aliasing and amplitude distortions. The proposed approach is then extended to the design of multichannel cosine-modulated QMF banks with low reconstruction delays, which are often required, especially in real-time applications. Several design examples are included to demonstrate the proposed algorithms, and some comparisons are made with existing designs     

A new iterative diakoptics-based multilevel moments method forplanar circuits

This paper combines a multilevel moments method (MMM) scheme with a modified diakoptics (MD) technique and a block Gauss-Seidel (BGS) iterative technique to reduce the solution time of large planar microwave structures. The proposed MMM scheme has two levels. On the lower level, the planar circuit is divided into several subcircuits using two types of artificial ports. At the higher level, general basis functions defined over the complete circuit are generated in an iterative way. The validity and the efficiency of the new technique are validated by several examples, including a large low-pass filter     

A dynamic convergence analysis of blind equalization algorithms

Blind equalizers do not require a training sequence to start up or to restart after a communications breakdown, making them particularly useful in applications such as broadcast and point-to-multipoint networks. We study in parallel the dynamic convergence behavior of three blind equalization algorithms: the multimodulus algorithm (MMA), the constant modulus algorithm (CMA), and the reduced constellation algorithm (RCA). Using a conditional Gaussian approximation, we first derive the theoretical mean-squared-error (MSE) trajectory for MMA. This analysis leads to accurate but somewhat cumbersome expressions. Alternatively, we apply a Taylor series approximation to derive MSE trajectories for MMA, CMA, and RCA. This approach yields simpler but somewhat less accurate expressions. For the steady-state operation, however we derive even simpler formulas that accurately predict the asymptotic MSE values. We finally study the convergence rates of the three blind algorithms using their theoretical MSE trajectories, computer simulations, and a laboratory experiment     

Improved Newton-type algorithm for adaptive implementation ofPisarenko's harmonic retrieval method and its convergence analysis

Pisarenko's harmonic retrieval (PHR) method is probably the first eigenstructure based algorithm for estimating the frequencies of sinusoids corrupted by additive white noise. To develop an adaptive implementation of the PHR method, one group of authors has proposed a least-squares type recursive algorithm. In their algorithm, they made approximations for both gradient and Hessian. The authors derive an improved algorithm, where they use exact gradient and a different approximation for the Hessian and analyze its convergence rigorously. Specifically, they provide a proof for the local convergence and detailed arguments supporting the local instability of undesired stationary points. Computer simulations are used to verify the convergence performance of the new algorithm. Its performance is substantially better than that exhibited by its counterpart, especially at low SNR's     

Global convergence of Newton's method in the DC analysis of single-transistor networks

Global convergence of Newton's method is proved for the DC equations of a one-transistor network. Sufficient conditions are also given for global convergence in networks of n transistors.     

On-line SVD-based iterative method for signal recovery fromnonuniform samples

An on-line iterative method for signal recovery from nonuniform samples is presented. This method uses the singular value decomposition (SVD) approach to estimate both the uniform samples and the error in their estimation. Two examples of its application are given     

An image dependent stopping method for iterative denoising procedures

Iterative methods are very successful for denoising images corrupted by random valued impulse noise. However, choosing the optimal number of iterations is a difficult issue. In this letter, a stopping method is proposed: the iterative denoising process is stopped when the number of cleaned pixels is minimal. It corresponds to the moment when the denoising process tends to modify noise-free pixels. It also corresponds with a high precision to the maximum of PSNR of the restored image. The originality of the method is that no a priori iteration number is to be chosen but the method results from image information. The proposed stopping strategy is therefore an efficient and image dependent method that can be easily implemented on real data.