The projection method for solving nonlinear systems of equations under the ''most violated constraint'' control (Q1069671)

This paper analyzes an extended version of \textit{S. Kaczmarz}' method [Bull. Inst. Acad. Polon. Sci. A 1937, 355-357 (1937; Zbl 0017.31703)] for solving nonlinear algebraic equations. The method is related to those of \textit{K.-H. Meyn} [Numer. Math. 42, 161-172 (1983; Zbl 0497.65026)] and the reviewer [Indiana Univ. Math. J. 26, 1137-1150 (1977; Zbl 0341.65046) and Numer. Math. 23, 371-385 (1975; Zbl 0303.65046)], but with the major improvement that the equations are treated generally by blocks. It is characterized by the use of local linearization in turn on each block that ``most'' violates the corresponding equations. The method is analyzed theoretically with convergence rate estimates. Some numerical results are also reported.