On Newton’s Method for Convex Functions and Operators and its Relationship with Contraction Principle
Keywords:successive approximations, contraction principle, symmetric operators, convex operators, global Newton method
In this review paper, generally known results on a version of global Newton’s method for convex increasing or decreasing functions and operators, as well as afferent examples and applications, are recalled. Connection with the contraction principle is discussed in detail and applied to approximate , Where is a positive invertible symmetric operator acting on a finite-dimensional Hilbert space, and is a real number. Two numerical examples for symmetric matrices with real coefficients are given. Some other nonlinear matrix or scalar equations are solved approximately.
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