Starting from disjoint disks which contain polynomial complex zeros, the new iterative interval method for simultaneous finding of inclusive disks for complex zeros is formulated. The convergence theorem and the conditions for convergence are considered, and the convergence is shown to be fourth. Numerical examples are included.
Given a continuous real-valued function f which vanishes outside a fixed finite interval, we establish necessary conditions for weighted mean convergence of Lagrange interpolation for a general class of even weights w which are of exponential decay on the real line or at the endpoints of (-1,1).
Let S n [f] be the nth partial sum of the orthonormal polynomials expansion with respect to a Freud weight. Then we obtain sufficient conditions for the boundedness of S n [f] and discuss the speed of the convergence of S n [f] in weighted L p space. We also find sufficient conditions for the boundedness of the Lagrange interpolation polynomial L n [f], whose...
Let w exp(-Q), where Q is of faster than smooth polynomial growth at ~, for example, w k,α (x) exp(-exp k (|x| α )),α>1. We obtain a necessary and sufficient condition for mean convergence of Lagrange interpolation for such weights in L p (0<p=<1) completing earlier investigations by the first author and D.S. Lubinsky in L p (1<p<~).
An average interpolation is introduced for 3-rectangles and tetrahedra, and optimal order error estimates in the H 1 norm are proved. The constant in the estimate depends ''weakly'' (improving the results given in Duran (Math. Comp. 68 (1999) 187-199) on the uniformity of the mesh in each direction. For tetrahedra, the constant also depends on the maximum angle of the element. On the other...
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