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A constructive iterative procedure for solving operator equations. (English. Russian original) Zbl 0833.47053
Comput. Math. Math. Phys. 34, No. 11, 1469-1475 (1994); translation from Zh. Vychisl. Mat. Mat. Fiz. 34, No. 11, 1710-1718 (1994).
Summary: An iterative procedure for solving operator equations of general form in Banach spaces by means of which the problem of solving a nonlinear equation reduces to solving equations with almost linear continuous operators, is described. For a wide class of equations in Hilbert space, a constructive iterative procedure which can be used to solve the initial problem is described and the conditions under which it converges to the exact solution are obtained.
MSC:
47J25 Iterative procedures involving nonlinear operators
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