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We consider frequency‐weighted damping optimization for vibrating systems described by a second‐order differential equation. The goal is to determine viscosity values such that eigenvalues are kept away from certain undesirable areas on the imaginary axis. To this end, we present two complementary techniques. First, we propose new frameworks using nonsmooth constrained optimization problems, whose...
We present a new algorithm for solving the eigenvalue problem for an n×n real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in O(n2) operations under certain circumstances. The algorithm is based on a shift-and-invert approach. Only a single element of the inverse of the shifted matrix eventually...
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