On Convergence of Sequences of Interpolating Polynomials

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We have studied relations between approximated continuous functions f and places of nodes of interpolating polynomials for f. We have two main results. One is that functions which can be approximated by any sequence of interpolating polynomials obtained by increasing nodes are analytic. The other is that spline functions g with one knot are expressed as the limit of a sequence of Hermite interpolating polynomials for some two nodes.