Rational Spectral Filters with Optimal Convergence Rate

In recent years, contour-based eigensolvers have emerged as a standard approach for the solution of large and sparse eigenvalue problems. Building upon performance improvements through non-linear least square optimization so-called rational filters, we introduce systematic method to design these filters by minimizing worst-case convergence ratio eliminate parametric dependence on weight functions. Further, provide an efficient way deal with box-constraints which play central role use iterative linear solvers in eigensolvers. Indeed, parameter-free consistently minimize number iterations FLOPs reach eigensolver. As byproduct, our allow simple load balancing when interior eigenproblem is approached slicing sought after spectral interval.