For a family of gradient methods on quadratics, the iterates asymptotically zigzag between the extreme eigenvectors; a new stepsize converging to 1/λn breaks the zigzag and yields a competitive periodic method.
Cauchy , M´ ethode g´ en´ erale pour la r´ esolution des systemes d’´ equations simultan´ ees, Comp
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On the asymptotic convergence and acceleration of gradient methods
For a family of gradient methods on quadratics, the iterates asymptotically zigzag between the extreme eigenvectors; a new stepsize converging to 1/λn breaks the zigzag and yields a competitive periodic method.