Fast Monte Carlo Method for Condition Number Estimation
DOI:
https://doi.org/10.55630/dipp.2021.11.21Keywords:
Monte Carlo Method, Markov Chain, Condition Number, EigenvalueAbstract
This paper presents theoretical results on estimation the condition number with application in image restoration problems.References
Chan, S. (2010). Constructing a sparse convolution matrix for shift varying image restoration problems. ICIP 2010. in Proc. IEEE.
Dimov, I., & Karaivanova, A. (1998). Parallel computations of eigenvalues based on a Monte Carlo approach. Monte Carlo Methods and Applications, 4 (1), 33-52.
Dimov, I., Philippe, B., Karaivanova, A., & Weihrauch, C. (2008). Robustness and applicability of Markov chain Monte Carlo algorithms for eigenvalue problems. Applied Mathematical Modelling, (8), 1511-1529. doi:http://dx.doi.org/10.1016/j.apm.2007.04.012
Golub, G., & Van Loon, C. (1996). Matrix Computation. Baltimore: The Johns Hopkins University Press.
Isaacson, E., & Keller, H. (1996). Analysis of Numerical Methods. Dover Publications, INC.N.Y.
Kaposi, G., Szkaliczki, T., Márkus, Z. L., Luchev, D., Goynov, M., & Paneva- Marinova, D. (2013). Mobile Exploring of the Bulgarian Iconography through QR Codes in the GUIDE@HAND Tourist Guide Application. International Conference on Digital Presentation and Preservation of Cultural and Scientific Heritage, September 18-21, 2013, Veliko Tarnovo, Bulgaria. III , pp. 44-52. Sofia: Institute of Mathematics and Informatics - BAS.
Kim, B. (2002). Numerical Optimization Methods for Image Restoration. Stanford University.
Stanley, H. C., Ankit, K., Truong, Q. N., & Edmund, Y. L. (2011). Bounds for the Condition Numbers of Spatially-variant Convolution Matrices in Image Restoration Problems. SMA4. Optical Society of America. doi:https://doi.org/10.1364/SRS.2011.SMA4
