"Interpolation" is a foundational mathematical treatise that explores the theory and practical application of estimating values between known data points. Authored by the esteemed mathematician J.F. Steffensen, this work provides a rigorous and comprehensive overview of the methods essential to numerical analysis and actuarial science. The text covers a wide array of topics, including the construction and use of interpolation formulas, the properties of divided differences, and the estimation of remainder terms to ensure mathematical precision.
Steffensen offers detailed derivations and proofs for central concepts such as Newton's formula, Stirling's formula, and Everett's formula, making the work both a theoretical resource and a practical guide. Special attention is given to the accuracy of approximations, with thorough discussions on error analysis and the limitations of various techniques. By addressing inverse interpolation and the application of these methods to complex data sets, "Interpolation" serves as an invaluable reference for mathematicians, statisticians, and engineers. This classic work stands as a testament to the development of numerical methods and remains a critical study for those seeking a deep understanding of mathematical approximation and its historical evolution.
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