Home Application of g-frames in conjugate gradient
Article
Licensed
Unlicensed Requires Authentication

Application of g-frames in conjugate gradient

  • Hassan Jamali EMAIL logo and Neda Momeni
Published/Copyright: June 15, 2016

Abstract

This paper proposes an iterative method for solving an operator equation on a separable Hilbert space H equipped with a g-frame. We design an algorithm based on the conjugate gradient method and investigate the convergence and optimality of this algorithm.

References

[1] Cheny C. C., Introduction to Approximation Theory, McGraw Hill, NY, 1966. Search in Google Scholar

[2] Christensen O., An Introduction to Frames and Riesz Bases, Birkhauser, Boston, 2003. 10.1007/978-0-8176-8224-8Search in Google Scholar

[3] Dahlke S., Fransier M. and Raasch T., Adaptive frame methods for operator equations, Advances in comp. Math. 27 (2007), 27–63. 10.1007/s10444-005-7501-6Search in Google Scholar

[4] Jamali H., Using canonical dual frames in adaptive Richardson iterative method for solving operator equations, Adv. Pure Appl. Math. 4 (2013), 251–263. 10.1515/apam-2013-0005Search in Google Scholar

[5] Stevenson R., Adaptive solution of operator equations using wavelet frames, SIAM J. Numer. Anal. 41 (2003), 1047–1100. 10.1137/S0036142902407988Search in Google Scholar

[6] Sun W., G-frames and G-Riesz bases, J. Math. Anal. Appl. 322 (2006), 437–452. 10.1016/j.jmaa.2005.09.039Search in Google Scholar

Received: 2016-3-1
Revised: 2016-5-28
Accepted: 2016-5-31
Published Online: 2016-6-15
Published in Print: 2016-7-1

© 2016 by De Gruyter

Downloaded on 18.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/apam-2016-0020/html
Scroll to top button