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Abstract
In this work we studied the problem of interpolation with spline functions and specially the problem of lacunary interpolation.
in the first chapter,we presented a general introduction through which we studied briefly the up-to-date results published in the international journals concerning the lacunary interpolation.
in the second chapter we presented some new methods for the interpolation with spline functions and proved the convergences.
in the third chapter we also presented new methods for the (0,2)lacunary interpolation when the values of the function and its second derivative are the only given values.we also proved the convergence theorems.
in the last chapter we tested the given methods numerically and we proved that the numerical results satisfy the theoritical ones.