Computational experience with quadratically convergent minimisation methods

A quadratically convergent VBSCF method.

A quadratically convergent valence bond self-consistent field method is described where the simultaneous optimisation of orbitals and the coefficients of the configurations (VB structures) is based on a Newton-Raphson scheme. The applicability of the method is demonstrated in actual calculations. The convergence and efficiency are compared with the Super-CI method. A necessary condition to achi...

Approximate Zeros of Quadratically Convergent Algorithms

Smale's condition for a point to be an approximate zero of a function for Newton's method is extended to the general quadratically convergent iterative algorithm. It is shown in which way the bound in the condition is affected by the characteristics of the algorithm. This puts the original condition of Smale for Newton's method in a more general perspective. The results are also discussed in th...

Neural Network Learning Through Optimally Conditioned Quadratically Convergent Methods Requiring NO LINE SEARCH

Neural Network Learning algorithms based on Conjugate Gradient Techniques and Quasi Newton Techniques such as Broyden, DFP, BFGS, and SSVM algorithms require exact or inexact line searches in order to satisfy their convergence criteria. Line searches are very costly and slow down the learning process. This paper will present new Neural Network learning algorithms based on Hoshino's weak line se...

Error bars and quadratically convergent methods for the numerical simulation of the Hartree-Fock equations

Quadratically convergent algorithms for optimal dextrous hand grasping

There is a robotic balancing task, namely real-time dextrous-hand grasping, for which linearly constrained, positive definite programming gives a quite satisfactory solution from an engineering point of view. We here propose refinements of this approach to reduce the computational effort. The refinements include elimination of structural constraints in the positive definite matrices, orthogonal...