TY - JOUR ID - 1023 TI - Application of frames in Chebyshev and conjugate gradient methods JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Jamali, H. AU - Afroomand, E. AD - Department of mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. Y1 - 2017 PY - 2017 VL - 43 IS - 5 SP - 1265 EP - 1279 KW - Hilbert spaces‎ KW - ‎dual space‎ KW - ‎frame‎ KW - ‎Chebyshev polynomials‎ KW - ‎iterative method‎ DO - N2 - ‎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. UR - http://bims.iranjournals.ir/article_1023.html L1 - http://bims.iranjournals.ir/article_1023_0cb1da24283448175d3dd2f38ccde208.pdf ER -