A Globally Convergent Ball Newton Method
Copyright policy )A Globally Convergent Ball Newton Method
A new n-dimensional Newton method is presented. In each step a whole n-dimensional ball is determined rather than a single new approximation point. This ball contains the desired zero of the given function. The method is globally convergent. If the given initial ball does not contain any zero, then the method stops after a finite number of steps. Depending upon the assumptions which are made, the convergence of the ball radii is linear, superlinear or quadratic.
Newton's method, convergence, Numerical computation of solutions to systems of equations, Interval and finite arithmetic, ball Newton operator, interval arithmetic
Newton's method, convergence, Numerical computation of solutions to systems of equations, Interval and finite arithmetic, ball Newton operator, interval arithmetic
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