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...

An intensive use of the bicycle may increase the risk of erectile dysfunction and the compression of the perineal area has been showed to be a major mechanism leading to sexual alterations compromising the quality of life. Manufacturers claim that pads contribute to increase cyclists perineal protection ensuring a high level of comfort. To investigate the influence of various cycling pads with ...

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...