Problem Of Poor Convergence Research Articles

SOURCE LOCALIZATION WITH MINIMAL NUMBER OF NETWORKED SENSORS

Based on concentration measurements from spatially distributed electronic noses, the location of a point source is to be determined. It is assumed that the emitted substance is transported by advection caused by a known homogeneous wind field and by diffusion. A new two-step approach for solving the source localization problem is presented. The new approach overcomes the problem of poor convergence of iterative algorithms, which try to minimize the least squares output error. Finally the problem of minimal sensor number and optimal sensor placement is investigated.

Source localization by spatially distributed electronic noses for advection and diffusion

Based on continuous concentration measurements from spatially distributed electronic noses, the location of a point source is to be determined. It is assumed that the emitted substance is transported by advection caused by a known homogeneous wind field and by isotropic diffusion. A new two-step approach for solving the source localization problem is presented. In the first step, for each sensor i, the set of points P/sub i/ is determined, on which the source can lie, taking only the specific concentration measurement C/sub i/ at sensor i into account. In the second step, an estimate for the source position is evaluated by intersecting the sets P/sub i/. The new approach overcomes the problem of poor convergence of iterative algorithms, which try to minimize the least squares output error. Finally, experimental results showing the capability of the new approach are presented.

An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition

An accurate and efficient solution method using spectral collocation method with domain decomposition is proposed for computing optical waveguides with discontinuous refractive index profiles. The use of domain decomposition divides the usual single domain into a few subdomains at the interfaces of discontinuous refractive index profiles. Each subdomain can be expanded by a suitable set of orthogonal basis functions and patched at these interfaces by matching the physical boundary conditions. In addition, a new technique incorporating the effective index method and the Wentzel-Kramers-Brillouin method for the a-priori determination of the scaling factor in Hermite-Gauss or Laguerre-Gauss basis functions is introduced to considerably save computational time without experimenting with it. This method shares the same desirable property of the spectral collocation method of providing a fast and accurate solution but avoids the oscillatory solutions and improves the poor convergence problem of the simple spectral collocation method with single domain where regions of discontinuous refractive index profiles exist. Applications to several two- and three-dimensional waveguide structures having exact or accurate approximate solutions are given to test the accuracy and efficiency; all the results are found to be in excellent agreement.

Layered 4D representation and voting for grouping from motion

We address the problem of perceptual grouping from motion cues by formulating it as a motion layers inference from a sparse and noisy point set in a 4D space. Our approach is based on a layered 4D representation of data, and a voting scheme for token communication, within a tensor voting computational framework. Given two sparse sets of point tokens, the image position and potential velocity of each token are encoded into a 4D tensor. By enforcing the smoothness of motion through a voting process, the correct velocity is selected for each input point as the most salient token. An additional dense voting step allows for the inference of a dense representation in terms of pixel velocities, motion regions, and boundaries. Using a 4D space for this tensor voting approach is essential since it allows for a spatial separation of the points according to both their velocities and image coordinates. Unlike most other methods that optimize certain objective functions, our approach is noniterative and, therefore, does not suffer from local optima or poor convergence problems. We demonstrate our method with synthetic and real images, by analyzing several difficult cases-opaque and transparent motion, rigid and nonrigid motion, curves and surfaces in motion.

Accuracy analysis for wavelet approximations

"Constructive wavelet networks" are investigated as a universal tool for function approximation. The parameters of such networks are obtained via some "direct" Monte Carlo procedures. Approximation bounds are given. Typically, it is shown that such networks with one layer of "wavelons" achieve an L(2) error of order O(N(-(rho/d))), where N is the number of nodes, d is the problem dimension and rho is the number of summable derivatives of the approximated function. An algorithm is also proposed to estimate this approximation based on noisy input-output data observed from the function under consideration. Unlike neural network training, this estimation procedure does not rely on stochastic gradient type techniques such as the celebrated "backpropagation" and it completely avoids the problem of poor convergence or undesirable local minima.

Poor convergence in applying an optimal integral regulator to a system with a RHS zero

Necessary and sufficient conditions of the optimal regulator incorporating integral feedback were given by Porter Ill and Smith and Davison [2]. This note presents a problem of poor convergence in an iterative solution of the discrete Riccati equations when an optimal regulator incorporating <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r = m</tex> integral feedback is applied to a system which has a zero on the RHS of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</tex> -plane, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> are the input and output dimensions, respectively. The problem of poor convergence was clarified by simulation studies and analytically examined based on certain assumptions. The poor convergence is due to poor choice of an initial guess in the above special situation. However, this problem is very important from a practical point of view because the initial guess is difficult in the first stage of regulator design.

Some interesting features of spherical cap transducers

Interesting features of spherical caps have been identified and investigated as a result of the availability of large computers which has overcome the problem of poor convergence of the wave‐harmonic series for spherical cap directivity at large ka. Caps which have radial velocity excitation exhibit Fresnel diffraction effects for ka ⩾ 2π. The presence of these effects has been verified experimentally with a spherical transducer which shows an axial loss of sensitivity for conditions corresponding to the 2nd Fresnel half‐period zone. Fresnel theory predicts the occurrence of directivity extrema for caps which are hemispherical or smaller. Data for prediction of diffraction effects for larger caps is presented for 2π ⩽ ka ⩽ 20π. Axially excited caps do not exhibit diffraction effects. The velocity coefficients for the wave‐harmonic series for axial velocity excitation are developed. Axially excited hemispherical caps were observed to exhibit constant directivity index for ka ⩾ 0.8π. [Work partially supported by NAVSEA and NCSC.]