Interpolation by a sum of exponential functions when some exponents are preassigned
Recently [J. Approximation Theory 34, 194-210 (1982)] the author has solved two interpolation problems. The first one is for equidistant nodes and the other for confluent nodes and in each case interpolation is by a sum of exponential functions where none of the exponents are known. Necessary and sufficient conditions for the existence and uniqueness of their solutions and explicit formulae were given in terms of the corresponding Padé approximants. Here the author generalizes these results by specifying some of the exponents. Again he obtains necessary and sufficient conditions for existence and uniqueness of the solutions and also gives the explicit form of the solutions when some of the exponents are known. Using the connection with Padé approximation, he also proves that under certain conditions, the discrete case converges to the confluent case.
scientific article; zbMATH DE number 3951187
scientific article