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A new interpolation formula in the form of a continued fraction

Research paper by B. Michalík

Indexed on: 01 Jul '83Published on: 01 Jul '83Published in: Czechoslovak Journal of Physics



Abstract

An interpolation formula in the form of a continued fraction is derived. In the limit case, where the table points are equal, it turns into an expansion of the function into a continued fraction near the point. The formula can be a useful tool for interpolating singular functions. As an application, a series of methods for solving non-linear equations is derived, the first two of them being identical with the methods by Halley and Kiss.