The convergence of the class of direct interpolatory iterationsI n for a simple zero of a non-linear operatorF in a Banach space of finite or infinite dimension is studied.
A general convergence result is established and used to show that ifF is entire the “radius of convergence” goes to infinity withn while ifF is analytic in a ball of radiusR the radius of convergence increases to at leastR/2 withn.
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The research was supported in part by the National Science Foundation under Grant MCS 75-222-55 and the office of Naval Research under Contract N00014-76-C-0370, NR 044-422.
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Traub, J.F., Woźniakowski, H. Optimal radius of convergence of interpolatory iterations for operator equations. Aeq. Math. 21, 159–172 (1980). https://doi.org/10.1007/BF02189351
AMS (1970) subject classification
- Primary 47H10, 47H15, 65J05, 68A20