ON THE STEEPEST DESCENT APPROXIMATION TO SOLUTIONS OF NONLINEAR STRONGLY ACCRETIVE OPERATOR EQUATIONS

A new inequality of Banach spaces and the asymptotic stability theory on the equilibrium point of a certain type of initial value problem are used to establish the global convergence of the steepest descent approximation for accretive operator equations. Let X be a real uniformly smooth Banach space...

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Veröffentlicht in:Journal of computational mathematics 1992-10, Vol.10, p.173-182
Hauptverfasser: Zong-ben, Xu, Bo, Zhang, Roach, G.F.
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description A new inequality of Banach spaces and the asymptotic stability theory on the equilibrium point of a certain type of initial value problem are used to establish the global convergence of the steepest descent approximation for accretive operator equations. Let X be a real uniformly smooth Banach space and A: X ➝ X be a demicontinuous, strongly accretive operator. It is proved under suitable assumptions on an that the iterative process xn+1 = xn - anAxn, x₀ ϵ X, n = 0, 1, 2,··· converges strongly to the unique solution of the equation Ax = 0. The theorem obtained generalises and improves several existing results.
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title ON THE STEEPEST DESCENT APPROXIMATION TO SOLUTIONS OF NONLINEAR STRONGLY ACCRETIVE OPERATOR EQUATIONS
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