An Optimally Generalized Steepest-Descent Algorithm for Solving Ill-Posed Linear Systems
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-12-17
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
It is known that the steepest-descent method converges normally at the first few iterations, and then it slows down.
We modify the original steplength and descent direction by an optimization argument with the new steplength as being a merit function to be maximized.
An optimal iterative algorithm with m-vector descent direction in a Krylov subspace is constructed, of which the m optimal weighting parameters are solved in closed-form to accelerate the convergence speed in solving ill-posed linear problems.
The optimally generalized steepest-descent algorithm (OGSDA) is proven to be convergent with very fast convergence speed, accurate and robust against noisy disturbance, which is confirmed by numerical tests of some well-known ill-posed linear problems and linear inverse problems.
American Psychological Association (APA)
Liu, Chein-Shan. 2013. An Optimally Generalized Steepest-Descent Algorithm for Solving Ill-Posed Linear Systems. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-15.
https://search.emarefa.net/detail/BIM-450156
Modern Language Association (MLA)
Liu, Chein-Shan. An Optimally Generalized Steepest-Descent Algorithm for Solving Ill-Posed Linear Systems. Journal of Applied Mathematics No. 2013 (2013), pp.1-15.
https://search.emarefa.net/detail/BIM-450156
American Medical Association (AMA)
Liu, Chein-Shan. An Optimally Generalized Steepest-Descent Algorithm for Solving Ill-Posed Linear Systems. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-15.
https://search.emarefa.net/detail/BIM-450156
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-450156