scholarly journals Construction of the solutions of linear operator equations in Banach spaces

1991 ◽  
Vol 43 (10) ◽  
pp. 1247-1254
Author(s):  
A. A. Boichuk ◽  
V. F. Zhuravlev
Keyword(s):  
Linear Operator ◽  
Banach Spaces ◽  
Operator Equations ◽  
Linear Operator Equations

scholarly journals Minimization of Tikhonov Functionals in Banach Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
Author(s):  
Thomas Bonesky ◽  
Kamil S. Kazimierski ◽  
Peter Maass ◽  
Frank Schöpfer ◽  
Thomas Schuster
Keyword(s):  
Linear Operator ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Dual Space ◽  
Descent Method ◽  
The Other ◽  
Steepest Descent Method ◽  
Operator Equations ◽  
Underlying Space ◽  
Linear Operator Equations

Tikhonov functionals are known to be well suited for obtaining regularized solutions of linear operator equations. We analyze two iterative methods for finding the minimizer of norm-based Tikhonov functionals in Banach spaces. One is the steepest descent method, whereby the iterations are directly carried out in the underlying space, and the other one performs iterations in the dual space. We prove strong convergence of both methods.

On nonnegative solvability of linear operator equations

1994 ◽  
Vol 18 (1) ◽  
pp. 88-108 ◽  
Author(s):  
Ruey-Jen Jang-Lewis ◽  
Harold Dean Victory
Keyword(s):  
Linear Operator ◽  
Operator Equations ◽  
Linear Operator Equations
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