The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
Adaptive Multiprecision Path Tracking
SIAM Journal on Numerical Analysis
Accurate evaluation of a polynomial and its derivative in Bernstein form
Computers & Mathematics with Applications
Reducing rounding errors and achieving Brouwer's law with Taylor Series Method
Applied Numerical Mathematics
Accurate evaluation of the k-th derivative of a polynomial and its application
Journal of Computational and Applied Mathematics
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In the paper, we examine the local behavior of Newton's method in floating point arithmetic for the computation of a simple zero of a polynomial assuming that an good initial approximation is available. We allow an extended precision (twice the working precision) in the computation of the residual. We prove that, for a sufficient number of iterations, the zero is as accurate as if computed in twice the working precision. We provide numerical experiments confirming this.