P. Turan and his associates considered in detail the problem of (0.2) interpolation based on the zeros of πn(x). Motivated by these results and an earlier result of Szabados and Varma[9] here we consider the problem ...P. Turan and his associates considered in detail the problem of (0.2) interpolation based on the zeros of πn(x). Motivated by these results and an earlier result of Szabados and Varma[9] here we consider the problem of existence, uniqueness and explicit representation of the interpolatory polynomial Rn (x) satisfying the function values at one set of nodes and the second derivative on the other set of nodes. It is important to note that this problem has a unique solution provided these two sets of nodes are chosen properly. We also promise to have an interesting convergence theorem in the second paper of this series, which will provide a solution to the related open problem of P. Turan.展开更多
文摘P. Turan and his associates considered in detail the problem of (0.2) interpolation based on the zeros of πn(x). Motivated by these results and an earlier result of Szabados and Varma[9] here we consider the problem of existence, uniqueness and explicit representation of the interpolatory polynomial Rn (x) satisfying the function values at one set of nodes and the second derivative on the other set of nodes. It is important to note that this problem has a unique solution provided these two sets of nodes are chosen properly. We also promise to have an interesting convergence theorem in the second paper of this series, which will provide a solution to the related open problem of P. Turan.
