On a nontraditional method of approximation

Interpolation by generalized exponential sums with equal weights

“…Formulas similar to (38) were obtained in [8,13]. Again, they require more arithmetic operations than (38), although have almost the same interpolation rate, O(z n ).…”

“…on |S m | equivalently). For example, it was proved in [8], that the condition |s m | a m implies that |σ m | a m , where m = 1, . .…”

“…Main theorem about the Padé interpolation by H n . Recall the definitions (1) and (8) and the assumptions (5), (6) and (7). Theorem 3.…”

“…are usually called h-sums; they were introduced in [13]. The most explored case is η = 1, λ k h(λ k z), λ k ∈ C, see [6,8,9,13,14,16,22]. The paper [13] contains several remarks 1 on the general case (3).…”

“…We are interested in solving the following Padé (multiple) interpolation problem in a neighbourhood of z = 0: find complex µ and {λ k } n k=1 , depending on f, h and n, such that (8) f (z) − H n (z; h) = O(z n+1 ) for z → 0.…”