On the method of tangent hyperbolas on Banach spaces
Journal of Computational and Applied Mathematics
Matrix computations (3rd ed.)
Historical developments in convergence analysis for Newton's and Newton-like methods
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
An acceleration of Newton's method: Super-Halley method
Applied Mathematics and Computation
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
On large-scale unconstrained optimization problems and higher order methods
Optimization Methods & Software - The 2nd Veszprem Optimization Conference: Advanced Algorithms (VOCAL), 13-15 December 2006, Veszprem, Hungary
An efficient version on a new improved method of tangent hyperbolas
LSMS'07 Proceedings of the Life system modeling and simulation 2007 international conference on Bio-Inspired computational intelligence and applications
On the Halley class of methods for unconstrainedoptimization problems
Optimization Methods & Software - The 2nd International Conference on Nonlinear Programming with Applications
Rate of convergence of higher order methods
Applied Numerical Mathematics
Rate of convergence of higher order methods
Applied Numerical Mathematics
| Hi-index | 7.29 |
We consider solving the unconstrained minimization problem using an iterative method derived from the third order super Halley method. Each iteration of the super Halley method requires the solution of two linear systems of equations. We show a practical implementation using an iterative method to solve the linear systems. This paper introduces an array of arrays (jagged) data structure for storing the second and third derivative of a multivariate function and suitable termination criteria for the (inner) iterative method to achieve a cubic rate of convergence. Using a jagged compressed diagonal storage of the Hessian matrices and for the tensor, numerical results show that storing the diagonals are more efficient than the row or column oriented approach when we use an iterative method for solving the linear systems of equations.