Some Approximated Solutions for Operator Equations by Using Frames
-
2441
Downloads
-
3570
Views
Authors
H. Jamali
- Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Kerman, Iran.
Abstract
In this paper we give some approximated solutions for an operator equation \(Lu=f\) where \(L: H\rightarrow H\) is a bounded and self adjoint operator on a separable Hilbert space \(H\). We use frames in order to precondition the linear equation so that convergence of iterative methods is improved. Also we find an exact solution associated to a frame and then we seek an approximated solution in a finite dimensional subspace of \(H\) that is generated by a finite frame sequence.
Share and Cite
ISRP Style
H. Jamali, Some Approximated Solutions for Operator Equations by Using Frames, Journal of Mathematics and Computer Science, 12 (2014), no. 2, 105-112
AMA Style
Jamali H., Some Approximated Solutions for Operator Equations by Using Frames. J Math Comput SCI-JM. (2014); 12(2):105-112
Chicago/Turabian Style
Jamali, H.. "Some Approximated Solutions for Operator Equations by Using Frames." Journal of Mathematics and Computer Science, 12, no. 2 (2014): 105-112
Keywords
- Operator equation
- Separable Hilbert space
- Frame
- Approximated solution.
MSC
References
-
[1]
K. G. Atkinson, Iterative variants of the Nystrom method for the numerical solution ofintegral equations, Numer. Math., 22 (1973), 17-31.
-
[2]
M. Bahmanpour, M. A. Friborzi Araghi , Numerical solution of Fredholmand Volterraintegral equation of the first kind using wavelets bases, J. Math. Computer Sci., 5 (2012), 337-345.
-
[3]
W. Briggs , A Multigrid Tutorial, society for Industrial and Applied Mayhematics, Philadelphia, PA (1987)
-
[4]
P. G. Casazza, The art of frame theory, Taiwaness J. Math., 4 (2000), 129-201.
-
[5]
O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, Boston (2003)
-
[6]
A. Cohen, W. Dahmen, R. DeVore, Adaptive wavelet methods for elliptic operator equations:convergence rates , Math. of comp. , 70:233 (2001), 27-75.
-
[7]
A. Cohen, W. Dahmen, R. DeVore, Adaptive wavelets methods II-beyond the elliptic case, Found. of Comp. Math. , 2 (2002), 203-245.
-
[8]
S. Dahlek, M. Fornasier, T. Raasch, Adaptive frame methods for elliptic operator equations, Advances in comp. Math. , 27 (2007), 27-63.
-
[9]
S. Dahlek, T. Raasch, M. Werner, Adaptive frame methods for elliptic operator equations:the steepest descent approach, IMA J. Numer. Anal. , 27 (2007), 717-740.
-
[10]
M. M. Shamaooshaky, P. Asghari, H. Adibi, The numerical solution of non linier Fredholm-Hammerstein integral equation of the second kind utilizing Chebyshev wavelets, J. Math. Computer Sci., 10 (2014), 235-246.
-
[11]
R. Stevenson, Adaptive solution of operator equations using wavelet frames, SIAM J. Numer.Anal. , 41 (2003), 1074-1100.