Doubly exponential convergence of the cyclic steepest descent method for strictly convex quadratics in arbitrary dimensions

This arXiv paper investigates the cyclic steepest descent (CSD) method for strictly convex quadratic minimization problems. The CSD method performs j consecutive iterations using the exact steepest descent step size computed at the beginning of each cycle. The authors prove doubly exponential convergence of the cycle-starting gradient sequence for arbitrary dimensions, extending previous results that were restricted to two-dimensional cases. This theoretical contribution advances the understanding of optimization algorithms commonly used in scientific computing and machine learning training pipelines.