An augmented singular transform and its partial Newton method for finding new solutions Academic Article

abstract

• 2015 Elsevier B.V. All rights reserved. To find new solutions through the information provided by previously found solution(s), this paper is first to develop a new singular transform to change the local basin-barrier structure of the original problem in an infinite-dimensional space and then to propose an augmented partial Newton method to solve the transformed problem on the solution set. Mathematical justifications of the new formulation and method are established. Details on algorithm implementation are presented. Examples for two very different variational PDE problems are carried out to illustrate the method. Their numerical results are displayed by profile-contour plots and error/convergence data. The formulation and method developed in this paper can also be applied to solve multiple fixed point problems.

authors

• Zhou, Jianxin

published proceedings

• Journal of Computational and Applied Mathematics

author list (cited authors)

• Xie, Z., Yi, W., & Zhou, J.

citation count

• 4

complete list of authors

• Xie, Ziqing||Yi, Wenfan||Zhou, Jianxin

publication date

• January 2015

publisher

• Elsevier  Publisher

published in

• Journal of Computational and Applied Mathematics  Journal

Digital Object Identifier (DOI)

• 10.1016/j.cam.2015.02.049

start page

• 145

end page

• 157

volume

• 286

URL

• http://dx.doi.org/10.1016/j.cam.2015.02.049