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Applications of Polynomial Interpolation

Explore the diverse applications of polynomial interpolation and extrapolation in mathematics, typography, computer science, and physics. From numerical differentiation to typography shapes determination, discover the significance of interpolation in various fields.

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Applications of Polynomial Interpolation

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  1. Marija Stanojevic SI 2010/0011 Applications of Polynomial Interpolation and Extrapolation

  2. Application to Mathematics - Neville's algorithm is used in numerical differentiation - Interpolation is used for evaluation of natural logarithm and trigonometric functions - Polynomial interpolation is essential for quadratic multiplication and squaring such as Karatsuba multiplication and Toom-Cook multiplication

  3. Applications to Typography - Interpolation algorithms are used to determine shapes of letters in typography given a few points

  4. Application to Computer Science - Polynomial interpolation forms bases for algorithms in Secure Multiparty Computation and Secret Sharing schemes - Extrapolation is used for iterative reconstruction in digital imaging, called interior reconstruction - Interpolation is used for optimization of sparse random graphs

  5. Application to Physics - Interpolation is used to prove the existence of so-called free energy thermodynamic limits for several spin glass models - Geophysical data with noise and gaps in coverage is processed using interpolation to reduce noise and improve pictures

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