A variety of second-order accurate, in both space and time, full and approximate factorization methods for the numerical solution of two-dimensional reaction-diffusion equations is presented. These methods may use tim...
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A variety of second-order accurate, in both space and time, full and approximate factorization methods for the numerical solution of two-dimensional reaction-diffusion equations is presented. These methods may use time linearization and yield linearly implicit techniques and one-dimensional operators in each direction. It is shown that, if the factorization errors are neglected, linearly implicit approximate factorization methods provide uncoupled equations, whereas, if these errors are considered, the equations are coupled and must be solved iteratively. It is also shown that the allocation of the reaction and diffusion terms to the one-dimensional operators plays a paramount role in determining the accuracy of approximate factorization methods and preserving the symmetry of the original differential problem. Iterative, full and approximate factorization methods that do require iterations are also presented, and, for the problem considered here, these methods are shown to converge in about two iterations and provide solutions in agreement with those obtained with linearly implicit full and approximate factorization techniques. (c) 2005 Elsevier Inc. All rights reserved.
The problems of extending the J-lossless conjugation, the (J,J')-spectral factorization, and the (J,J')-lossless factorization to a completely general discrete-time system are considered. Existence conditions ...
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The problems of extending the J-lossless conjugation, the (J,J')-spectral factorization, and the (J,J')-lossless factorization to a completely general discrete-time system are considered. Existence conditions together with a numerically-sound prototype algorithm for computing the factors are provided for a system having any type of singularity, including arbitrary normal rank, poles and zeros at infinity, at zero, or on the unit circle. (C) 2013 Elsevier Ltd. All rights reserved.
Linearizations of nonlinear functions that are based on Jacobian matrices often cannot be applied in practical applications of nonlinear estimation techniques. An alternative linearization method is presented in this ...
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Linearizations of nonlinear functions that are based on Jacobian matrices often cannot be applied in practical applications of nonlinear estimation techniques. An alternative linearization method is presented in this paper. The method assumes that covariance matrices are determined on a square root factored form. A factorization of the output covariance from a nonlinear vector function is directly determined by "perturbing" the nonlinear function with the columns of the factored input covariance, without explicitly calculating the linearization and with no differentiations involved. The output covariance is more accurate than that obtained with the ordinary Jacobian linearization method. It also has an advantage that Jacobian matrices do not have to be derived symbolically. (C) 1997 Elsevier Science Ltd.
In this paper several new methods for estimating scene structure and camera motion from an image sequence taken by affine cameras are presented. All methods can incorporate both point, line and conic features in a uni...
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In this paper several new methods for estimating scene structure and camera motion from an image sequence taken by affine cameras are presented. All methods can incorporate both point, line and conic features in a unified manner. The correspondence between features in different images is assumed to be known. Three new tensor representations are introduced describing the viewing geometry for two and three cameras. The centred affine epipoles can be used to constrain the location of corresponding points and conics in two images. The third order, or alternatively, the reduced third order centred affine tensors can be used to constrain the locations of corresponding points, lines and conics in three images. The reduced third order tensors contain only 12 components compared to the 16 components obtained when reducing the trifocal tensor to affine cameras. A new factorization method is presented. The novelty lies in the ability to handle not only point features, but also line and conic features concurrently. Another complementary method based on the so-called closure constraints is also presented. The advantage of this method is the ability to handle missing data in a simple and uniform manner. Finally, experiments performed on both simulated and real data are given, including a comparison with other methods.
Introducing the associated Bessel polynomials in terms of two non-negative integers, and under an integrability condition we simultaneously factorize their corresponding differential equation into a product of the lad...
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Introducing the associated Bessel polynomials in terms of two non-negative integers, and under an integrability condition we simultaneously factorize their corresponding differential equation into a product of the ladder operators by four different ways as shape invariance symmetry equations. This procedure gives four different pairs of recursion relations on the associated Bessel polynomials. In spite of description of Bessel and Laguerre polynomials in terms of each other, we show that the associated Bessel differential equation is factorized in four different ways whereas for Laguerre one we have three different ways. (c) 2006 Elsevier B.V. All rights reserved.
In this article a novel recursive method for estimating structure and motion from image sequences is presented. The novelty lies in the fact that the output of the algorithm is independent of the chosen coordinate sys...
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In this article a novel recursive method for estimating structure and motion from image sequences is presented. The novelty lies in the fact that the output of the algorithm is independent of the chosen coordinate systems in the images as well as the ordering of the points. It relies on subspace and factorization methods and is derived from both ordinary coordinate representations and camera matrices and from a so-called depth and shape analysis. In addition, no initial phase is needed to start the algorithm. It starts directly with the first two images and incorporates new images as soon as new corresponding points are obtained. The performance of the algorithm is shown on both simulated and real data. Moreover, the two different approaches, one using camera matrices and the other using the concepts of affine shape and depth, are unified into a general theory of structure and motion from image sequences. (C) 1999 Elsevier Science B.V. All rights reserved.
In this paper the problem of finite input/output representation of a special class of nonlinear Volterra polynomial systems is studied via the notion of linear factorization of delta-series. This is an algebraic metho...
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In this paper the problem of finite input/output representation of a special class of nonlinear Volterra polynomial systems is studied via the notion of linear factorization of delta-series. This is an algebraic method based mainly on the star-product operation and on a related Euclidean-type algorithm. (C) 1997 Elsevier Science Ltd.
This paper presents a new method for factoring a self-inversive Hermitian matrix polynomial relative to the unit-radius circle. It formulates the factorization problem as that of evaluating a set of definite integrals...
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This paper presents a new method for factoring a self-inversive Hermitian matrix polynomial relative to the unit-radius circle. It formulates the factorization problem as that of evaluating a set of definite integrals along the unit circle and of solving a block-Toeplitz system of linear equations. Since the evaluation of definite integrals along the unit circle can be accomplished via parallel computations and the solution of a block-Toeplitz system can be obtained by a fast algorithm, the proposed method is very useful in real-time applications.
Two forms of Friedland's separate bias estimation algorithm with U-D factorization of the covariance matrices are provided. Each is suited to implementation in a particular computing environment. (We consider MATL...
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Two forms of Friedland's separate bias estimation algorithm with U-D factorization of the covariance matrices are provided. Each is suited to implementation in a particular computing environment. (We consider MATLAB and compiled computer languages.) We reduce the computation time substantially, primarily at the time propagation stage, by using a separated bias formulation, while retaining the desirable numerical properties of the U-D factorization. The perecentage reduction typically increases with ratio of bias state dimension to dynamic state dimension. A numerical evaluation is given for the MATLAB algorithm.
In this paper the problem of finite input-output representation is sol, ed for a class of Finite Degree Discrete Volterra Systems containing cross products among inputs and outputs, via the so-called delta epsilon-ope...
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In this paper the problem of finite input-output representation is sol, ed for a class of Finite Degree Discrete Volterra Systems containing cross products among inputs and outputs, via the so-called delta epsilon-operators. A corresponding algorithm is supplied. An application concerning the bilinear systems is also given.
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