Generalized riesz method and convergence acceleration

Abstract

Several propositions on A‐boundedness for generalized Riesz method (5ft, P_n), where P_n are linear bounded operators from Banach space X into X, are proved. These results are applied to study convergence acceleration using generalized Riesz method and generalized Zygmund method.

Straipsnyje irodyta keletas teiginiu, susijusiu su A aprežtumu apibendrintam Rieszo metodui, kai P_n yra tiesinis aprežtasis operatorius Banacho erdveje X. Šie rezultatai taikomi tiriant Rieszo ir apibendrinto Zygmundo metodu konvergavimo pagreiti.

Key words:

• linear summability methods
• convergence acceleration
• Tauberian remainder theorems