Convergence analysis of a block preconditioned steepest descent eigensolver with implicit deflation

Gradient-type iterative methods for solving Hermitian eigenvalue problems can be accelerated by using preconditioning and deflation techniques. A preconditioned steepest descent iteration with implicit (PSD-id) is one of such methods. The convergence behavior the PSD-id recently investigated based on pioneering work Samokish method (PSD). resulting non-asymptotic estimates indicate a superlinear under strong assumptions initial guess. present paper utilizes an alternative analysis PSD Neymeyr much weaker assumptions. We embed Neymeyr's approach into restricted formulation PSD-id. More importantly, we extend new to practically preferred block version PSD-id, or BPSD-id, show cluster robustness BPSD-id. Numerical examples are provided validate theoretical estimates.