Approximated Solutions to Operator Equations based on the Frame Bounds

Authors

  • H. Jamali Department of Mathematics, Vali-e-Asr University, Rafsanjan, Kerman
  • A. Askari Hemmat Department of Mathematics, Shahid Bahonar University of Kerman, Kerman; Department of Mathematics, Kerman Graduate University of Technology, Kerman; International Center for Science and High Technology and Environment Sciences, Kerman

DOI:

https://doi.org/10.26713/cma.v3i3.209

Keywords:

Operator equation, Hilbert space, Frame, Approximated solution

Abstract

We want to find the solution of the problem ${\L} u = f$, based on knowledge of frames. Where ${\L} : H \to H$ is a boundedly invertible and symmetric operator on a separable Hilbert space $H$. Inverting the operator can be complicated if the dimension of $H$ is large. Another option is to use an algorithm to obtain approximations of the solution. We will organize an algorithm in order to find approximated solution of the problem depends on the knowledge of some frame bounds and the guaranteed speed of convergence also depends on them.

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References

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CITATION

How to Cite

Jamali, H., & Hemmat, A. A. (2012). Approximated Solutions to Operator Equations based on the Frame Bounds. Communications in Mathematics and Applications, 3(3), 253–259. https://doi.org/10.26713/cma.v3i3.209

Issue

Vol. 3 No. 3 (2012)

Section

Research Article

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