# Application of frames in Chebyshev and conjugate gradient methods

Document Type: Research Paper

Authors

Department of mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

Abstract

‎Given a frame of a separable Hilbert space $H$‎, ‎we present some‎ ‎iterative methods for solving an operator equation $Lu=f$‎, ‎where $L$ is a bounded‎, ‎invertible and symmetric‎ ‎operator on $H$‎. ‎We present some algorithms‎ ‎based on the knowledge of frame bounds‎, ‎Chebyshev method and conjugate gradient method‎, ‎in order to give some‎ ‎approximated solutions to the problem‎. ‎Then we investigate the‎ ‎convergence and optimality of them.

Keywords

Main Subjects

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### History

• Receive Date: 31 August 2015
• Revise Date: 29 January 2016
• Accept Date: 22 May 2016