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In this paper, we propose generalized inverse power methods with variable shifts for finding the smallest H-/Z-eigenvalue and associated H-/Z-eigenvector of symmetric tensors. The methods are guaranteed to always converge to a H-/Z-eigenpair. Furthermore, for an even order nonsingular symmetric M -tensor, the proposed method with any positive initial point always converges to the smallest H-eigenvalue. Numerical results are reported to illustrate that the proposed methods often can find the smallest H-/Z-eigenvalue instead of other H-/Z-eigenvalues of symmetric tensors. Moreover, we can always get the smallest H-eigenvalue for an even order nonsingular symmetric M -tensor. [ABSTRACT FROM AUTHOR]

Simulating soft matter systems such as the cytoskeleton can enable deep understanding of experimentally observed phenomena. One challenge of modelling such systems is realistic description of the steric repulsion between nearby polymers. Previous models of the polymeric excluded volume interaction have the deficit of being non-analytic, being computationally expensive, or allowing polymers to erroneously cross each other. A recent solution to these issues, implemented in the MEDYAN simulation platform, uses analytical expressions obtained from integrating an interaction kernel along the lengths of two polymer segments to describe their repulsion. Here, we extend this model by re-deriving it for lower-dimensional geometrical configurations, deriving similar expressions using a steeper interaction kernel, comparing it to other commonly used potentials, and showing how to parameterise these models. We also generalise this new integrated style of potential by introducing a segmental Lennard-Jones potential, which enables modelling both attractive and repulsive interactions in semi-flexible polymer networks. These results can be further generalised to facilitate the development of effective interaction potentials for other finite elements in simulations of softmatter systems. [ABSTRACT FROM AUTHOR]

In this paper, a new alternating direction trust region method based on conic model is used to solve unconstrained optimization problems. By use of the alternating direction search method, the new conic model trust region subproblem is solved by two steps in two orthogonal directions. This new idea overcomes the shortcomings of conic model subproblem which is difficult to solve. Then the global convergence of the method under some reasonable conditions is established. Numerical experiment shows that this method may be better than the dogleg method to solve the subproblem, especially for large-scale problems. [ABSTRACT FROM AUTHOR]

In this paper, we compute Z-eigenvalues of a class of tensors by studying the properties of semi-symmetric tensor. We prove that A x m − 1 is identical to zero if and only if A s = 0 , where A s is the associated semi-symmetric tensor of A . Based on the semi-symmetric property, an almost nonnegative irreducible tensor is defined. And we use Newton method to compute Z-eigenvalues of this kind of tensor. The convergence of the proposed algorithm can be guaranteed. Numerical results are reported to illustrate the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

We present a new cubic convergent method for solving a system of nonlinear equations. The new method can be viewed as a modified Chebyshev's method in which the difference of Jacobian matrixes replaces three order tensor. Therefore, the new method reduces the storage and computational cost. The new method possesses the local cubic convergence as well as Chebyshev's method. A rule is deduced to ensure the descent property of the search direction, and a nonmonotone line search technique is used to guarantee the global convergence. Numerical results indicate that the new method is competitive and efficient for some classical test problems. [ABSTRACT FROM AUTHOR]