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Recursion Relation (recursion + relation)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

Designer polynomials, discrete variable representations, and the Schrödinger equation

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4-5 2002
Charles A. Weatherford
Abstract The general procedure for constructing a set of orthonormal polynomials is given for an arbitrary positive definite weight function, w(x), in the interval [a, b]. The Lanczos method is used to generate the three-term recursion relation, which is then used to produce the polynomial coefficients. A discrete variable representation (DVR) is constructed from Gaussian nodes and weights that result from the three-term recursion relation. These are termed "designer polynomials" and the associated "designer DVRs." It will be shown by construction that every such set of "synthetic polynomials" carries an associated DVR. The term "designer" derives from the fact that the interval [a, b] and the weight function w(x) are arbitrary (except that w(x) must be positive definite on [a, b] and must have continuous derivatives except at a finite number of isolated discontinuities) and may be adapted to the physical problem of interest. The difficulties of applying a DVR to a "bare" Coulomb problem will be illustrated on a "toy" model in one dimension (1-D hydrogen atom). A solution for the 1-D Coulomb problem will be given, thereby motivating the need for designer DVRs. In doing so, a new set of polynomials is defined with a weight function w(x) = |x|kexp(,,|x|), (such that k = ,1, 0, +1, +2, ,) between the symmetrical limits [,,, +,]. These are called "synthetic Cartesian exponential polynomials (SCEP)." These polynomials are then used in a spectral and pseudospectral (DVR) representation to solve the 1-D hydrogen atom problem. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source]

Alternative formulation and applications aspects of the generalized projection method for array antenna synthesis

INTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 6 2009
E. Botha
Abstract An array synthesis technique is formulated, which implements the method of generalized projections in the array excitation space. This permits the use of relaxation in the overall recursion relation that is not possible with previous formulations, resulting in accelerated convergence for slowly converging problems. Weighted least squares is introduced as a backward operator in an integral way that enhances the method. Means are described for determining starting points that assist the synthesis algorithm in avoiding so-called traps. The results obtained for a diverse selection of applications of the method are discussed. These demonstrate the effects on convergence of the use of relaxation, different pattern sampling angle selection schemes, and different starting point selection schemes. © 2009 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009. [source]

MAP fusion method for superresolution of images with locally varying pixel quality

INTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 4 2008
Kio Kim
Abstract Superresolution is a procedure that produces a high-resolution image from a set of low-resolution images. Many of superresolution techniques are designed for optical cameras, which produce pixel values of well-defined uncertainty, while there are still various imaging modalities for which the uncertainty of the images is difficult to control. To construct a superresolution image from low-resolution images with varying uncertainty, one needs to keep track of the uncertainty values in addition to the pixel values. In this paper, we develop a probabilistic approach to superresolution to address the problem of varying uncertainty. As direct computation of the analytic solution for the superresolution problem is difficult, we suggest a novel algorithm for computing the approximate solution. As this algorithm is a noniterative method based on Kalman filter-like recursion relations, there is a potential for real-time implementation of the algorithm. To show the efficiency of our method, we apply this algorithm to a video sequence acquired by a forward looking sonar system. © 2008 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 18, 242,250, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). [source]

Analysis of optical and terahertz multilayer systems using microwave and feedback thoery

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 5 2009
Dong-Joon Lee
Abstract The principles of microwave and feedback theory are independently applied to the analysis of both optical and terahertz-regime multilayer systems. An analogy between the two approaches is drawn, and useful recursion relations, along with a signal-flow approach, are presented for both reflection and transmission cases. These relations, in terms of S-parameters, allow an exact analytical solution for even arbitrary, active, stratified structures, not only for any wavelength in the radio-frequency spectrum, but also for optical wavelengths. This approach also provides a bridge between the microwave and optical bands and leads to beneficial design solutions for intermediate bands such as the THz regime. Comparisons with conventional methodologies are provided using practical multilayer simulations. In addition, graphical design techniques from microwave theory are used along with examples for efficient design and understanding. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 1308,1312, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24301 [source]