Because 3-D data are acquired using 3-D sensing such as stereo vision and laser range finders, they have inhomogeneous and anisotropic noise. This paper studies optimal computation of the similarity (rotation, translation, and scale change) of such 3-D data. We first point out that the Gauss-Newton and the Gauss-Helmert methods, regarded as different techniques, have similar structures. We then...

|This paper proposes a feedback structure for the design of l 2-stable algorithms for nonlinear adaptive lter-ing and identiication, and establishes explicit connections between classical schemes in IIR modeling and more recent results in H 1-theory. In particular, two algorithms due to Feintuch (1976) and Landau (1979), as well as the so-called pseudo-linear regression and Gauss-Newton algorit...

Abstract. It was shown by P. J. Davis that the Newton-Cotes quadrature formula is convergent if the integrand is an analytic function that is regular in a sufficiently large region of the complex plane containing the interval of integration. In the present paper, a bound on the error of the Newton-Cotes quadrature formula for analytic functions is derived. Also the bounds on the Legendre polyno...

A method for estimating the position, shape and 3-D motion of the human head from a multiview image sequence is presented. Threedimensional motion is estimated by using an approach which also takes into consideration the photometric e ects of motion, assuming a specular illumination re ection model. Gauss-Newton optimization is used to estimate the illumination and 3-D motion parameters. An ell...

K e y w o r d s G a u s s N e w t o n ' s method, Lipschitz conditions with L average, Convergence ball, Uniqueness bali. 1. I N T R O D U C T I O N Finding the solution of a nonlinear operator equation f(x) = 0 (1.1) in Banach space X is a very general subject which is widely used in both theoretical and applied areas of mathematics, where f is a nonlinear operator from some domain D in a real...

In this paper we consider the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed inverse problems. Under merely Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an order optimal regularization method if the solution is regular in some suitable sense.

In this letter, the problem of adaptive tracking the amplitude and phase of a noisy sinusoid with known frequency is addressed. Based on approximating the recursive Gauss–Newton approach, two computationally simple algorithms, which provide direct parameter estimates, are devised and analyzed. Simulation results show that the proposed methods can attain identical estimation performance as their...

In this paper, we develop and demonstrate a new 2 order two-stage algorithm called OWO-Newton. First, two-stage algorithms are motivated and the Gauss Newton input weight Hessian matrix is developed. Block coordinate descent is used to apply Newton’s algorithm alternately to the input and output weights. Its performance is comparable to Levenberg-Marquardt and it has the advantage of reduced co...

We propose a generic method for iteratively approximating various second-order gradient steps - Newton, Gauss-Newton, Levenberg-Marquardt, and natural gradient - in linear time per iteration, using special curvature matrix-vector products that can be computed in O(n). Two recent acceleration techniques for on-line learning, matrix momentum and stochastic meta-descent (SMD), implement this appro...

This paper addresses the blind separation of convolutive mixtures of independent and non-Gaussian sources. We present a block-based Gauss-Newton algorithm which is able to obtain a separation solution using only a specific set of output cross-cumulants and the hypothesis of soft mixtures. The order of the cross-cumulants is chosen to obtain a particular form of the Jacobian matrix that ensures ...