This paper describes a set of numerical optimization algorithms for solving the GPS based attitude determination problem We pose the problem as one of minimizing the function tr N Q W with respect to SO where N Q andW are given matrices The method of steepest descent and Newton s method are generalized to SO by taking advantage of its Lie group structure Analytic solutions to the line search pr...

Steepest Descent. Discrete Iterative Optimization. Markov Chain Monte Carlo (MCMC). NOTE: NOT FOR DISTRIBUTION!!

Thispaperdescribes a set ofnumericalgradient-basedoptimizationalgorithmsfor solvingtheGlobalPositioning System (GPS)-based attitude determination problem. We pose the problem as one of minimizing the function tr( H N H TQ ¡ 2 H W)with respect to the rotation matrix H , where N, Q, andW are given 3 £ 3 matrices, and tr( ¢ ) denotes thematrix trace. Both the method of steepest descent and Newton’...

Augmented Downhill Simplex Method (ADSM) is introduced here, that is a heuristic combination of Downhill Simplex Method (DSM) with Random Search algorithm. In fact, DSM is an interpretable nonlinear local optimization method. However, it is a local exploitation algorithm; so, it can be trapped in a local minimum. In contrast, random search is a global exploration, but less efficient. Here, rand...

This paper proposes a query expansion method using fuzzy abductive inference for creative thinking support system. This query expansion method for information retrieval is useful, because unexpected related information are probably be obtained by adding new words to the query. The fuzzy abductive inference is the inference method based on Peng and Reggia's abductive inference. This method infer...

The purpose of this article is to give a streamlined and selfcontained treatment of the long-time asymptotics of the Toda lattice for decaying initial data in the soliton and in the similarity region via the method of nonlinear steepest descent.

This paper compares the use of firstand second-order Sobolev gradients to solve differential equations using the method of least-squares steepest descent. The use of high-order Sobolev gradients offers a very effective preconditioning strategy for the linear part of a nonlinear differential equation. 2005 Elsevier Ltd. All rights reserved.

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Toda lattice for decaying initial data in the soliton region. In addition, we point out how to reduce the problem in the remaining region to the known case without solitons.