Unconstrained optimization problems are closely related to systems of ordinary differential equations (ODEs) with gradient structure. In this work, we prove results that apply to both areas. We analyze the convergence properties of a trust region, or Levenberg–Marquardt, algorithm for optimization. The algorithm may also be regarded as a linearized implicit Euler method with adaptive timestep f...

We classify and review existing algorithms for computing the fundamental matrix from point correspondences and propose new effective schemes: 7-parameter Levenberg-Marquardt (LM) search, EFNS, and EFNS-based bundle adjustment. Doing experimental comparison, we show that EFNS and the 7-parameter LM search exhibit the best performance and that additional bundle adjustment does not increase the ac...

We describe a technique for solving for the orbital elements of multiple planets from radial velocity (RV) and/or astrometric data taken with 1 m/s and μas precision, appropriate for efforts to detect Earth-massed planets in their stars’ habitable zones, such as NASA’s proposed Space Interferometry Mission. We include details of calculating analytic derivatives for use in the Levenberg-Marquard...

BP Neural Network has a longer training time and a slow convergence. To deal with the defects of BP Neural Network a modified BP algorithm is proposed in the paper. The algorithm is applied for the control of Inverted Pendulum, a highly non linear system inherently being open loop unstable. Levenberg-Marquardt algorithm is used for the training purpose. The training samples are being collected ...

In this paper, the problem of nonnegative matrix factorization (NMF) is considered. It is formulated as the optimization of a criterion with bound constraints. We propose an approach based on Givens parameterization of some positive vector, and criterion minimization is achieved using Levenberg-Marquardt algorithm. The performance of the developed NMF method is illustrated for the separation of...

We study the global behaviour of a Newton algorithm on the Grassmann manifold for invariant subspace computation. It is shown that the basins of attraction of the invariant subspaces may collapse in case of small eigenvalue gaps. A Levenberg-Marquardt-like modification of the algorithm with low numerical cost is proposed. A simple strategy for choosing the parameter is shown to dramatically enl...

This paper proposes a novel application of Grammatical Bee Colony for classification of medical data. Grammatical Bee Colony is a Swarm Programming algorithm generally used for automatic computer program generation in any arbitrary language. In this paper, Grammatical Bee Colony based classifier is designed and applied in medical data mining. The proposed method is applied on ten medical data s...

This paper considers REML (residual or restricted maximum likelihood) estimation for heteroscedastic linear models. An explicit algorithm is given for REML-scoring which yields the REML estimates together with their standard errors and likelihood values. The algorithm includes a Levenberg-Marquardt restricted step modification which ensures that the REML-likelihood increases at each iteration. ...

This paper proposes a novel application of Grammatical Bee Colony for classification of medical data. Grammatical Bee Colony is a Swarm Programming algorithm generally used for automatic computer program generation in any arbitrary language. In this paper, Grammatical Bee Colony based classifier is designed and applied in medical data mining. The proposed method is applied on ten medical data s...

This paper proposes a novel application of Grammatical Bee Colony for classification of medical data. Grammatical Bee Colony is a Swarm Programming algorithm generally used for automatic computer program generation in any arbitrary language. In this paper, Grammatical Bee Colony based classifier is designed and applied in medical data mining. The proposed method is applied on ten medical data s...