A new HSS-like iterative method is first proposed based on HSS-like splitting of nonHermitian (1,1) block for solving saddle point problems. The convergence analysis for the new method is given. Meanwhile, we consider the solution of saddle point systems by preconditioned Krylov subspace method and discuss some spectral properties of the preconditioned saddle point matrices. Numerical experimen...

Within the harmonic approximation to transition state theory, the biggest challenge involved in finding the mechanism or rate of transitions is the location of the relevant saddle points on the multidimensional potential energy surface. The saddle point search is particularly challenging when the final state of the transition is not specified. In this article we report on a comparison of severa...

Many real world systems are at risk of undergoing critical transitions, leading to sudden qualitative and sometimes irreversible regime shifts. The development of early warning signals is recognized as a major challenge. Recent progress builds on a mathematical framework in which a real-world system is described by a low-dimensional equation system with a small number of key variables, where th...

Two variants of the extended Rosenbrock function are analyzed in order to find the stationary points. The first variant is shown to possess a single stationary point, the global minimum. The second variant has numerous stationary points for high dimensionality. A previously proposed method is shown to be numerically intractable, requiring arbitrary precision computation in many cases to enumera...

Introduction: Correction of Saddle nose deformity is one of the most challenging issues in facial plastic surgery.   Materials and Methods: In this study, a single structure in the form of L-strut was attempted to be created by using one 0.035" Kirschner wire and an autologous costal graft out of the 10th and 11th ribs. This study involved 13 cases, most of whom were traumatic. The corrective ...

We study the problem of coexistence of a countable number of periodic orbits of different topological types (saddles, saddle–centers, and elliptic) in the case of four-dimensional symplectic diffeomorphisms with a homoclinic trajectory to a saddle–focus fixed point.