Geodesic
The Analytic Character of the Birkhoff Interpolation Polynomials
Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 765-768

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Let E be an m ×(n + 1) regular interpolation matrix with elements ei, k = (E)i, k which are zero or one, with n + 1 ones. Then for each f ∈ Cn [a, b] and each set of knots X: a ≦ x 1 < ... < xm ≦ b, there is a unique interpolation polynomial P(f, E, X; t) of degree ≦ n which satisfies 1 A recent paper [1] discussed the continuity of P, as a function of x 1, ...,xm (with coalescences allowed). We would like to study in this note the analytic character of P as a function of real or complex knots X: x 1, ..., xm . This is easy for the Lagrange or the Hermite interpolation. In this case P is a polynomial in x 1, ..., xm if f is a polynomial, and an entire function in x 1, ..., xm if f is entire. 
Lorentz, G. G. The Analytic Character of the Birkhoff Interpolation Polynomials. Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 765-768. doi: 10.4153/CJM-1982-053-9
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[1] 1. Dyn, N., Lorentz, G. G. and Riemenschneider, S. D., Continuity of the Birkhoff interpolation, in print in SIAM J. Numer. Analysis. Google Scholar

[2] 2. Ferguson, D., The question of uniqueness for G. D. Birkhoff interpolation problem, J. Approx. Theory 2 (1969), 1–28. Google Scholar

[3] 3. Lorentz, G. G., Birkhoff interpolation problem, CNA report 103, The University of Texas in Austin (1975). Google Scholar

[4] 4. Lorentz, G. G., Independent sets of knots and singularity of interpolation matrices, J. Approx. Theory 30 (1980), 208–225. Google Scholar

[5] 5. Lorentz, G. G. and Riemenschneider, S. D., Recent progress in Birkhoff interpolation, in: Approximation theory and functional analysis (North-Holland Publ. Co., 1979, 187–236. Google Scholar

[6] 6. Lorentz, G. G. and Riemenschneider, S. D., Birkhoff interpolation: Some applications of coalescence, in : Quantitative approximation (Academic Press, New York), 1980–197. Google Scholar

[7] 7. Lorentz, G. G. and Zeller, K. L., Birkhoff interpolation problem: coalescence of rows, Arch. Math. 26 (1975), 189–192. Google Scholar

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