7,017 research outputs found
Some overview on unbiased interpolation and extrapolation designs
This paper considers the construction of optimal designs due to Hoel and
Levine and Guest. It focuses on the relation between the theory of the uniform
approximation of functions and the optimality of the designs. Some application
to accelerated tests is also presented. The multivariate case is also handled
in some special situations.Comment: 43 page
Newton's method in practice II: The iterated refinement Newton method and near-optimal complexity for finding all roots of some polynomials of very large degrees
We present a practical implementation based on Newton's method to find all
roots of several families of complex polynomials of degrees exceeding one
billion () so that the observed complexity to find all roots is between
and (measuring complexity in terms of number of
Newton iterations or computing time). All computations were performed
successfully on standard desktop computers built between 2007 and 2012.Comment: 24 pages, 19 figures. Update in v2 incorporates progress on
polynomials of even higher degrees (greater than 1 billion
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