CAJ | 학술논문

对于牛顿型迭代格式等经典的算法,近年来经过很多学者的研究已经取得了丰硕的理论成果,包括收敛性定理、Kantorovieh型定理和误差估计.局部收敛性定理需要假定了方程组有解,并且初始近似与解充分接近.然而对计算理论更为重要的是存在性、收敛性定理.在不知道解的情况下能够验证收敛条件,并且往往同时可以断定解的存在性乃至唯一性,因此对于各种迭代法建立存在性收敛性定理,始终是迭代法理论研究的中心课题之一.在Kantorovich型定理的条件下,给出了一种离散Newton型分裂方法的存在性及收敛性定理.
대우우돈형질대격식등경전적산법,근년래경과흔다학자적연구이경취득료봉석적이론성과,포괄수렴성정리、Kantorovieh형정리화오차고계.국부수렴성정리수요가정료방정조유해,병차초시근사여해충분접근.연이대계산이론경위중요적시존재성、수렴성정리.재불지도해적정황하능구험증수렴조건,병차왕왕동시가이단정해적존재성내지유일성,인차대우각충질대법건립존재성수렴성정리,시종시질대법이론연구적중심과제지일.재Kantorovich형정리적조건하,급출료일충리산Newton형분렬방법적존재성급수렴성정리.
Rich theoretical results of Newton-type iterative scheme and other classical algorithms have been made by many scholars in recent years, including convergence theorem, Kantorovich-type theorem and error estimate. The local convergence theorem requires the existence of solutions to nonlinear system of equations, and the initial approximation approaches the solution sufficiently. But the existence and convergence theorem is more important to the theory of computation. The convergence conditions can be verified in the case that the solution is unknown, and assert simultaneously the existence and uniqueness of the solution. Therefore, establishing the existence and convergence theorems for kinds of the iteration methods has always been one of the centers of theoretical analysis in iteration method. The Kantorovich theorem for discrete Newton-type decomposition methods is given.