We present how to use the block schur algorithm to design optical multi-layered filters. The block schur algorithm can, in turn, be applied to find reflection coefficients of optical multi-layered filters. We show tha...
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We present how to use the block schur algorithm to design optical multi-layered filters. The block schur algorithm can, in turn, be applied to find reflection coefficients of optical multi-layered filters. We show that the block schur algorithm using the block matrices is faster than the standard schur algorithm using the scalar elements on vector processor. The optimum sub-matrix size for the block schur algorithm on CRAY Y-MP C98 supercomputer is also suggested. (c) 2006 Elsevier B.V. All rights reserved.
In the first paper of this series (Daniel Alpay, Tomas Azizov, Aad Dijksma, and Heinz Langer: The schur algorithm for generalized schur functions I: coisometric realizations, Operator Theory: Advances and Applications...
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In the first paper of this series (Daniel Alpay, Tomas Azizov, Aad Dijksma, and Heinz Langer: The schur algorithm for generalized schur functions I: coisometric realizations, Operator Theory: Advances and Applications 129 (2001), pp. 1-36) it was shown that for a generalized schur function s(z), which is the characteristic function of a coisometric colligation V with state space being a Pontryagin space, the schur transformation corresponds to a finite-dimensional reduction of the state space, and a finite-dimensional perturbation and compression of its main operator. In the present paper we show that these formulas can be explained using simple relations between V and the colligation of the reciprocal s(z)(-1) of the characteristic function s(z) and general factorization results for characteristic functions.
This article extends the classical schur algorithm to matrix-valued functions that are bounded on the unit circle and have a finite number of Smith-McMillan poles inside the unit disc. With each such function this art...
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This article extends the classical schur algorithm to matrix-valued functions that are bounded on the unit circle and have a finite number of Smith-McMillan poles inside the unit disc. With each such function this article associates two infinite sequences: one is the well-known sequence of reflection coefficients (all less than one in magnitude), whereas the other is a sequence of signs. Under certain assumptions, the number of negative signs equals the number of poles within the unit disc. This article shows how to solve tangential interpolation problems using the algorithm and gives a simple proof for the connection between the number of poles inside the unit disc of each solution to the inertia of a certain Pick matrix. Also described is a numerically efficient procedure for carrying out the algorithm that involves only scalar operations.
We propose a design method for optical lattice filters using the schur algorithm in the z-transform domain. The algorithm of schur (on a power series bounded in the unit circle) is used for the one-dimensional inverse...
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ISBN:
(纸本)0819437395
We propose a design method for optical lattice filters using the schur algorithm in the z-transform domain. The algorithm of schur (on a power series bounded in the unit circle) is used for the one-dimensional inverse scattering problem to determine the reflection coefficients of multilayer medium modeled by the lattice filter. The proposed algorithm cart also be used to determine reflection coefficients in Fabrg-Perot etalons and multilayer thin film modeled by the lattice filter structure. We use the FFT method to find the transmission transfer function front transmission magnitude only. To verify the method, we give three simple examples.
作者：
Hu, YanjunHu, FangAnhui Univ
Minist Educ Key Lab Intelligent Comp & Signal Proc Hefei 230039 Anhui Peoples R China
A multiuser detector based on schur algorithm is studied in this paper. Because the computational complexity of the conventional decorrelating detector is high while computing the inverse of system matrices, especiall...
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ISBN:
(纸本)9781424436927
A multiuser detector based on schur algorithm is studied in this paper. Because the computational complexity of the conventional decorrelating detector is high while computing the inverse of system matrices, especially when the system is asynchronous and the number of users is huge. The simulation results show that the performance of the multiuser detector based on schur algorithm is similar to that of decorrelating detector, but it's computational complexity is much lower than decorrelating detector's.
A schur type algorithm for the lacunary Nehari problem making use of the extensions of certain isometrics is shown. A parametrization of the solution set is also obtained. A constructive method that provides the solut...
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A schur type algorithm for the lacunary Nehari problem making use of the extensions of certain isometrics is shown. A parametrization of the solution set is also obtained. A constructive method that provides the solutions by a sequence of schur type parameters is developed. In the case of the classical Nehari problem, this algorithm gives the classical schur parameters for the Carathéodory-Fejér interpolation problem. Here we propose another way to solve this problem, namely as an application of the Nehaii problem via the problem of the extension of isometrics associated to it. This point of view will lead in a forthcoming paper to the generalization of the results to the matricial case.
We propose a schur-type algorithm that includes spectral factorization of covariance matrix using circulant matrix factorization to design optical multimirror filters. The schur algorithm is the method used for a fast...
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We propose a schur-type algorithm that includes spectral factorization of covariance matrix using circulant matrix factorization to design optical multimirror filters. The schur algorithm is the method used for a fast Cholesky factorization of the Toeplitz matrix, which can determine the reflection coefficient of optical multimirror structures. Circulant matrix factorization is a very powerful tool used for spectral factorization from the covariance polynomial using matrix manipulation in vector space that can be found in the minimum phase polynomials without using the polynomial root finding method. We present a detailed description of the circulant matrix factorization for the reciprocal polynomial approximation of an arbitrary curve (or spectrum). The schur algorithm can, in turn, be applied to obtain the desired reflection coefficient of the optical filters. We also verify the performance of the proposed method by comparing it with the polynomial root finding method.
We 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 orth...
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We 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 & Sons, Ltd.
The nondegenerate truncated indefinite Stieltjes moment problem in the class N-k(k) of generalized Stieltjes functions is considered. To describe the set of solutions of this problem we apply the schur step-by-step al...
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The nondegenerate truncated indefinite Stieltjes moment problem in the class N-k(k) of generalized Stieltjes functions is considered. To describe the set of solutions of this problem we apply the schur step-by-step algorithm, which leads to the expansion of these solutions in generalized Stieltjes continuous fractions studied recently in [11]. Explicit formula for the resolvent matrix in terms of generalized Stieltjes polynomials is found. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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