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63
On the Lowrank Approximation by the Pivoted Cholesky Decomposition
, 2010
"... The consecutive numbering of the publications is determined by their chronological order. The aim of this preprint series is to make new research rapidly available for scientific discussion. Therefore, the responsibility for the contents is solely due to the authors. The publications will be distrib ..."
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Cited by 75 (3 self)
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The consecutive numbering of the publications is determined by their chronological order. The aim of this preprint series is to make new research rapidly available for scientific discussion. Therefore, the responsibility for the contents is solely due to the authors. The publications will be distributed by the authors.
Stability Issues In The Factorization Of Structured Matrices
 SIAM J. Matrix Anal. Appl
, 1997
"... . This paper provides an error analysis of the generalized Schur algorithm of Kailath and Chuna class of algorithms which can be used to factorize Toeplitzlike matrices, including blockToeplitz matrices, and matrices of the form T T T , where T is Toeplitz. The conclusion drawn is that if thi ..."
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Cited by 26 (5 self)
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. This paper provides an error analysis of the generalized Schur algorithm of Kailath and Chuna class of algorithms which can be used to factorize Toeplitzlike matrices, including blockToeplitz matrices, and matrices of the form T T T , where T is Toeplitz. The conclusion drawn is that if this algorithm is implemented with hyperbolic transformations in the factored form which is well known to provide numerical stability in the context of Cholesky downdating, then the generalized Schur algorithm will be stable. If a more direct implementation of the hyperbolic transformations is used, then it will be unstable. In this respect, the algorithm is analogous to Cholesky downdating; the details of implementation of the hyperbolic transformations are essential for stability. An example which illustrates this instability is given. This result is in contrast to the ordinary Schur algorithm for which an analysis by Bojanczyk, Brent and De Hoog shows that the stability of the algorithm is n...
Componentwise Analysis of Direct Factorization of Real Symmetric and Hermitian Matrices
 Linear Algebra Appl
, 1993
"... We derive componentwise backward error bound for the factorization H = GJG T , where H is a real symmetric matrix, G has full column rank, and J is diagonal with \Sigma1's on the diagonal. We also derive componentwise forward error bound, that is we bound the difference between the exact an ..."
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Cited by 20 (4 self)
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We derive componentwise backward error bound for the factorization H = GJG T , where H is a real symmetric matrix, G has full column rank, and J is diagonal with \Sigma1's on the diagonal. We also derive componentwise forward error bound, that is we bound the difference between the exact and the computed factor G, in the cases where such bound is possible. We extend these results to the Hermitian case, and to the wellknown BunchParlett factorization. Finally, we prove bounds for the scaled condition of the matrix G, and show that the factorization can have rank revealing property. 1. INTRODUCTION The n \Theta n real symmetric matrix H can be decomposed as H = GJG T ; (1.1) where G has full column rank, and J = diag (\Sigma1). Further, there is a permutation matrix P such that the matrix PG is lower block triangular Part of this work is contained in the author's Ph.D. thesis which was done at the Fernuniversitat Hagen. This work was also supported by the Grant No. 101252 ...
A PRIMALDUAL TRUST REGION ALGORITHM FOR NONLINEAR OPTIMIZATION
, 2003
"... This paper concerns general (nonconvex) nonlinear optimization when first and second derivatives of the objective and constraint functions are available. The proposed method is based on finding an approximate solution of a sequence of unconstrained subproblems parameterized by a scalar parameter. T ..."
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Cited by 18 (3 self)
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This paper concerns general (nonconvex) nonlinear optimization when first and second derivatives of the objective and constraint functions are available. The proposed method is based on finding an approximate solution of a sequence of unconstrained subproblems parameterized by a scalar parameter. The objective function of each unconstrained subproblem is an augmented penaltybarrier function that involves both primal and dual variables. Each subproblem is solved using a secondderivative Newtontype method that employs a combined trust region and line search strategy to ensure global convergence. It is shown that the trustregion step can be computed by factorizing a sequence of systems with diagonallymodified primaldual structure, where the inertia of these systems can be determined without recourse to a special factorization method. This has the benefit that offtheshelf linear system software can be used at all times, allowing the straightforward extension to largescale problems. Numerical results are given for problems in the COPS test collection.
On the feasibility of wireless shadowing correlation models
 IEEE Trans. Veh. Technol
, 2010
"... Abstract—There is emerging interest in more detailed models for wireless shadowing, which may include nonconstant shadowing variance, nonlognormal shadowing, and, most importantly, correlation between paths; we focus on this last aspect. This paper offers a structured synthesis of the existing lite ..."
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Cited by 16 (5 self)
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Abstract—There is emerging interest in more detailed models for wireless shadowing, which may include nonconstant shadowing variance, nonlognormal shadowing, and, most importantly, correlation between paths; we focus on this last aspect. This paper offers a structured synthesis of the existing literature on autocorrelation and crosscorrelation in wireless shadowing and attempts to fill existing gaps in the analysis of correlation models. We make a survey of these models and argue, as has previously been observed, that certain models are not mathematically feasible, which may lead to problems in simulations or analysis. We then state some theorems that test whether the models are positive semidefinite, which is the central necessary condition for feasibility, and evaluate the existing models accordingly. Additionally, we evaluate the models according to their physical plausibility, which leads us to choose one model among many as arguably the best one in existence so far. This paper should be useful as a guide on how to implement shadowing correlation in one’s work, how to choose an appropriate correlation model, and how to modify existing models or create new models so that they fulfill mathematical feasibility. Index Terms—Correlation, wireless channel modeling, wireless shadowing. I.
A parallel algorithm for computing the polar decomposition
 Parallel Computing
, 1994
"... Abstract. We propose an algorithm for computing the polar decomposition of a 3 × 3 real matrix that is based on the connection between orthogonal matrices and quaternions. An important application is to 3D transformations in the level 3 Cascading Style Sheets specification used in web browsers. Our ..."
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Cited by 15 (3 self)
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Abstract. We propose an algorithm for computing the polar decomposition of a 3 × 3 real matrix that is based on the connection between orthogonal matrices and quaternions. An important application is to 3D transformations in the level 3 Cascading Style Sheets specification used in web browsers. Our algorithm is numerically reliable and requires fewer arithmetic operations than the alternative of computing the polar decomposition via the singular value decomposition.
A square root unscented Kalman filter for visual monoSLAM
 in Proc. of the IEEE International Conference on Robotics and Automation
, 2008
"... Abstract — This paper introduces a Square Root Unscented Kalman Filter (SRUKF) solution to the problem of performing visual Simultaneous Localization and Mapping (SLAM) using a single camera. Several authors have proposed the conventional UKF for SLAM to improve the handling of nonlinearities compa ..."
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Cited by 14 (1 self)
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Abstract — This paper introduces a Square Root Unscented Kalman Filter (SRUKF) solution to the problem of performing visual Simultaneous Localization and Mapping (SLAM) using a single camera. Several authors have proposed the conventional UKF for SLAM to improve the handling of nonlinearities compared with the more widely used EKF, but at the expense increasing computational complexity from O(N 2) to O(N 3) in the map size, making it unattractive for videorate application. Van der Merwe and Wan’s general SRUKF delivers identical results to a general UKF along with computational savings, but remains O(N 3) overall. This paper shows how the SRUKF for the SLAM problem can be reposed with O(N 2) complexity, matching that of the EKF. The paper also shows how the method of inverse depth feature initialization developed by Montiel et al. for the EKF can be reformulated to work with the SRUKF. Experimental results confirm that the SRUKF and the UKF produce identical estimates, and that the SRUKF is more consistent than the EKF. Although the complexity is the same, the SRUKF remains more expensive to compute. I.