Showing papers on "Singular value decomposition published in 1970"
01 May 1970
TL;DR: In this article, the application of numerically stable matrix decompositions to minimization problems involving linear constraints is discussed and shown to be feasible without undue loss of efficiency, and the singular value decomposition is applied to the nonlinear least square problem and discusses related eigenvalue problems.
Abstract: The application of numerically stable matrix decompositions to minimization problems involving linear constraints is discussed and shown to be feasible without undue loss of efficiency. Part A describes computation and updating of the product-form of the LU decomposition of a matrix and shows it can be applied to solving linear systems at least as efficiently as standard techniques using the product-form of the inverse. Part B discusses orthogonalization via Householder transformations, with applications to least squares and quadratic programming algorithms based on the principal pivoting method of Cottle and Dantzig. Part C applies the singular value decomposition to the nonlinear least squares problem and discusses related eigenvalue problems.
73 citations
TL;DR: A novel iterative motion estimation algorithm that involves the anisotropic 3D uncertainty is proposed that is much more robust and fast than previous quasi-Newton optimization based approaches.
Abstract: Spatial anisotropic uncertainty of feature points must be taken into account to improve the precision in visual navigation. This paper includes two parts, which discuss error modeling and motion estimation respectively. In the first part we model the 3D reconstruction uncertainty in binocular stereo system as normal distribution and compute its propagation in stereo pair. Assume the uncertainty of image feature pixels geing normal distributed on the image plane, the reconstructed 3D error is analytically derived based on some error evaluation schemes. The closed-form solution of the 3D uncertainty is obtained for parallel camera setup. The second part of this paper proposes a novel iterative motion estimation algorithm that involves the anisotropic 3D uncertainty. We present a modified centroid coincidence theorem to divide the problem into two steps, rotation estimation and translation estimation. The translation estimation is straight-forward, and the latter can be obtained by a new iterative method as well. The LMS motion estimation criterion is linearized at 0th order and a motion estimation equation is proposed. The initial guess of the motion parameters is given by a SVD method. The iterative algorithm yields the optimal LMS motion estimation. Experimental data show that the iterative algorithm always converges under large and small point sets. It is much more robust and fast than previous quasi-Newton optimization based approaches. Transactions on Information and Communications Technologies vol 16, © 1996 WIT Press, www.witpress.com, ISSN 1743-3517
2 citations
TL;DR: In this paper, an inverse problem is studied for estimating the magnitude and direction of impact force acting on a body of arbitrary shape from strain responses measured at several points of the body.
Abstract: An inverse problem is studied for estimating the magnitude and direction of impact force acting on a body of arbitrary shape from strain responses measured at several points of the body. The noncausal Wiener filtering and the singular value decomposition are employed to improve the ill-conditioned nature of the inverse problem. The impact force acting on a simply supported beam subjected to transverse impact is estimated to verify the effectiveness of the inverse analysis.