Newton Interpolation Method for Data Completion

In data processing, missing values frequently occur and can compromise data accuracy and integrity if left unaddressed. One effective approach involves interpolation techniques, which leverage existing data patterns to estimate missing values. Newton interpolation stands as a prominent polynomial interpolation method that constructs a polynomial ranging from first to nth degree to approximate missing data points. The algorithm builds successive divided differences to form the interpolation polynomial, typically implemented through nested multiplication for computational efficiency. In practical applications, selection of interpolation methods should consider data characteristics and distribution patterns. Code implementations often utilize key functions like calculating divided difference tables and evaluating Newton polynomials using Horner's method for optimal numerical stability. Different interpolation strategies may be employed based on data types to achieve optimal results, with Newton's method particularly advantageous when adding new data points due to its incremental polynomial construction nature.