On the Hermite interpolation polynomial

Ovidiu Pop, Dan Barbosu


The Newton form for the Hermite interpolation polynomial using the divided differences with multiple knots is proved. Using this representation, su.cient conditions for the convergence of the sequence of Hermite interpolation polynomials are established. One extends this way a result obtained by M. Ivan, regarding to sufficient conditions for the uniform convergence of the sequence of Lagrange polynomials.

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