Biorthogonality of the Lagrange interpolants
نویسنده
چکیده
The Newton-Lagrange interpolation is a well-known problem in elementary calculus. Recall basic facts concerning this problem [6], [2]. Let Ak, k = 0, 1, 2, . . . and ak, k = 0, 1, 2, . . . be two arbitrary sequences of complex numbers (we assume that all ak are distinct ak 6= aj if k 6= j. By interpolation polynomial we mean a n-degree polynomial Pn(z) whose values at points a0, a1, . . . , an coincide with A0, A1, . . . , An, i.e. Pn(ak) = Ak, k = 0, 1, 2, . . . , n (1) Usually the parameters Ak are interpreted as values of some function F (z) at fixed points ak, i.e. Ak = F (ak) (2) In this case polynomials Pn(z) interpolate the function F (z) at points ak. Explicit expression for interpolation polynomial Pn(z) can be presented in two forms. In the Newtonian form we have [6], [2]
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