Steepest Descent for a Linear Operator Equation of the Second Kind with Application to Tikhonov Regularization
Dodd, T.J. and Harrison, R.F.
(2002)
Steepest Descent for a Linear Operator Equation of the Second Kind with Application to Tikhonov Regularization.
Research Report.
ACSE Research Report 827
.
Department of Automatic Control and Systems Engineering
Abstract
Let H1 H2 be Hilbert spaces, T a bounded linear operator on H1 into H2 such that the range of T, R (T), is closed. Lrt T* denote the adjoint of T. In this paper, we review the generalised solution and method of steepest descent, for the linear operator equation, Tx=b,b E H2. Further, we establish the convergence of the method of steepest descent to the unique solution (T*T=........
Metadata
Item Type:
Monograph
Authors/Creators:
Dodd, T.J.
Harrison, R.F.
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