An updated version of the Kantorovich theorem for Newton's method
Copyright policy )An updated version of the Kantorovich theorem for Newton's method
An affine invariant version of the Kantorovich theorem for Newton's method is presented. The result includes the Gragg-Tapia error bounds, as well as recent optimal and sharper upper bounds, new optimal and sharper lower bounds, and new inequalities showingq-quadratic convergence all in terms of the usual majorizing sequence. Closed form expressions for these bounds are given.
- University of Nevada Reno United States
- University of Nevada, Las Vegas United States
q-quadratic convergence, Iterative procedures involving nonlinear operators, Newton method, Numerical solutions to equations with nonlinear operators, Numerical computation of solutions to systems of equations, Gragg-Topia error bounds, Gragg-Tapia error bounds, Kantorovich theorem
q-quadratic convergence, Iterative procedures involving nonlinear operators, Newton method, Numerical solutions to equations with nonlinear operators, Numerical computation of solutions to systems of equations, Gragg-Topia error bounds, Gragg-Tapia error bounds, Kantorovich theorem
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