TY - JOUR
T1 - An Urabe type convergence theorem for a constructive simplified Newton method in infinite dimensional spaces
AU - Oishi, Shin'ichi
AU - Kashiwagi, Masahide
AU - Makino, Mitsunori
AU - Horiuchi, Kazuo
PY - 1991/12/1
Y1 - 1991/12/1
N2 - A constructive simplified Newton method is presented for calculating solutions of infinite dimensional nonlinear equations, which uses a projection scheme from an infinite dimensional space to finite dimensional subspaces. A convergence theorem of the method is shown based on Urabe's theorem. For a class of successive approximation methods containing an infinite dimensional homotopy method, a stopping criterion is shown using the convergence theorem. The authors show that under a certain condition the stopping criterion is satisfied in finite cycles of iteration.
AB - A constructive simplified Newton method is presented for calculating solutions of infinite dimensional nonlinear equations, which uses a projection scheme from an infinite dimensional space to finite dimensional subspaces. A convergence theorem of the method is shown based on Urabe's theorem. For a class of successive approximation methods containing an infinite dimensional homotopy method, a stopping criterion is shown using the convergence theorem. The authors show that under a certain condition the stopping criterion is satisfied in finite cycles of iteration.
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M3 - Conference article
AN - SCOPUS:0026299757
VL - 2
SP - 1236
EP - 1239
JO - Proceedings - IEEE International Symposium on Circuits and Systems
JF - Proceedings - IEEE International Symposium on Circuits and Systems
SN - 0271-4310
T2 - 1991 IEEE International Symposium on Circuits and Systems Part 4 (of 5)
Y2 - 11 June 1991 through 14 June 1991
ER -