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- W2314741446 abstract "Let E be an m × ( n + 1) regular interpolation matrix with elements e i , k = ( E ) i, k which are zero or one, with n + 1 ones. Then for each f ∈ C n [ a , b ] and each set of knots X : a ≦ x 1 < … < x m ≦ 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 , …, x m (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 , …, x m . This is easy for the Lagrange or the Hermite interpolation. In this case P is a polynomial in x 1 , …, x m if f is a polynomial, and an entire function in x 1 , …, x m if f is entire." @default.
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- W2314741446 date "1982-06-01" @default.
- W2314741446 modified "2023-09-30" @default.
- W2314741446 title "The Analytic Character of the Birkhoff Interpolation Polynomials" @default.
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- W2314741446 doi "https://doi.org/10.4153/cjm-1982-053-9" @default.
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