Numerical Methods

This section is about numerical methods. Main goal of this work is to study (and improve if possible) classical methods of numerical analysis from the digital signal processing point of view. Specifically I’m interested in the improvement of noise robustness properties of the widely used algorithms.

Research led me to the conclusion that usual least-square approximation which is basement of many methods cannot guarantee noise robustness in some cases. I’ve discovered new methods with guaranteed noise suppression for numerical differentiation, integration, interpolation, smoothing and missing data restoration.

Numerical Differentiation

Smooth noise-robust numerical differentiation.
Savitzky-Golay filters.
Central differences.

Numerical Integration

High-precision Gauss-Legendre Quadrature for C++ and MATLAB.
Cubature formulas for the unit disk.
Stable Newton-Cotes Formulas.
Stable Newton-Cotes Formulas (Open Type).
Overlapped Newton-Cotes Quadratures.

Data smoothing

Noise-robust smoothing filter (by Andrey Paramonov).

Multiprecision computing

High performance C++ interface for arbitrary precision arithmetic library – MPFR.

I’m planning to add information on other algorithms in the nearest future – so don’t forget to bookmark my site and come back later.

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