Abstract. We present a detailed convergence analysis of preconditioned MINRES for approximately solving the linear systems that arise when Rayleigh Quotient Iteration is used to compute the lowest eigenpair of a symmetric positive definite matrix. We provide insight into the “slow start” of MINRES iteration in both a qualitative and quantitative way, and show that the convergence of MINRES main...

The paper considers problem of buckling a thin elastic cylindrical shell, supported by rings various stiffness. approximate solution for clamping edge was obtained with analytical Rayleigh-Ritz method. parameters the optimal distribution mass structure between shell and stiffeners are found in order to maximize critical pressure. Frames zero eccentricity considered. solutions compared finite el...

As Henri PoincarC once remarked, “solution of a mathematical problem” is a phrase of indefinite meaning. Pure mathematicians sometimes are satisfied with showing that the non-existence of a solution implies a logical contradiction, while engineers might consider a numerical result as thc only reasonable goal. Such one sided views seem to reflect human limitations rather than objective values. I...