1,721,158 research outputs found
A constructive proof of the Gohberg-Semencul formula
No full textGohberg and Semencul gave some elegant formulas for the inverse of a Toeplitz matrix as a difference of products of lower and upper triangular Toeplitz matrices. There are several algebraic and analytic proof of these formulas. Here we give
Displacement structure for Hankel, Vandermonde, and related (derived) matrices
No full textAbstractWe introduce some generalized concepts of displacement structure for structured matrices obtained as products and inverses of Toeplitz, Hankel, and Vandermonde matrices. The Toeplitz case has already been studied at some length, and the corresponding matrices have been called near-Toeplitz or Toeplitz-like or Toeplitz-derived. We focus on Hankel- and Vandermonde-like matrices and in particular show how the appropriately defined displacement structure yields fast triangular and orthogonal factorization algorithms for such matrices. The main contribution of this paper is presenting a unified framework rather than obtaining the fastest algorithm for each special matrix
A nonlinear estimation algorithm and its optical implementation for target tracking in clutter environment
No full textThe two-dimensional tracking problem in a clutter environment is solved in the-discrete-time Bayes optimal (nonlinear, and non-Gaussian) estimation framework. The proposed method recursively finds the probability density functions of the target position and velocity. With our approach, the nonlinear estimation problem is converted into simpler linear convolution operations that can be implemented with optical devices efficiently. We present a possible optical implementation architecture, and its functionality is, verified through computer simulation
A Nonlinear Estimation Algorithm, and its Optical Implementation for the Target Tracking in Clutter Environment
No full textGeneralized Displacement Structure for Block-Toeplitz, Toeplitz-Block, and Toeplitz-Derived Matrices
No full textThe concept of displacement structure has been used to solve several problems connected with Toeplitz matrices and with matrices obtained in some way from Toeplitz matrices (e.g., by combinations of multiplication, inversion, and factorization). Matrices of the latter type will be called Toeplitz-derived (or Toeplitz-like, close-to-Toeplitz). This paper introduces a generalized definition of displacement for block-Toeplitz and Toeplitz-block arrays. It will turn out that Toeplitz-derived matrices are perhaps best regarded as particular Schur complements obtained from suitably defined block matrices. The new displacement structure is used to obtain a generalized Schur algorithm for fast triangular and orthogonal factorizations of all such matrices and well-structured fast solutions of the corresponding exact and overdetermined systems of linear equations. Furthermore, this approach gives a natural generalization of the so-called Gohberg-Semencul formulas for Toeplitz-derived matrices
The Schur algorithm applied to the design of optical multi-mirror structures
No full textWe show how to use the classical Schur algorithm to design multi-mirror optical interferometers (or filters). Our derivation is simple and straightforward, clearly revealing its connection to the previously known orthogonal digital filter structures. We also give a complete detailed description of an FFT-based algorithm for the reciprocal polynomial approximation of an arbitrary curve (or spectrum). The Schur algorithm can, in turn, be applied to the obtained polynomial to get the desired reflection coefficients of the mirrors. Copyright (c) 2004 John Wiley W Sons, Ltd
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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