section_path: Scientific work/Analysis/Numeric analysis
section_name: Numeric analysis
paragraph_text: Numeric analysis
  
  Gauss often deduced theorems inductively from numerical data he had collected empirically. As such, the use of efficient algorithms to facilitate calculations was vital to his research, and he made many contributions to numeric analysis, as the method of Gaussian quadrature published in 1816.
  
  In a private letter to Gerling from 1823, he described a solution of a 4X4 system of linear equations by using Gauss-Seidel method – an "indirect" iterative method for the solution of linear systems, and recommended it over the usual method of "direct elimination" for systems of more than two equations.
  
  Gauss invented an algorithm for calculating what is now called discrete Fourier transforms, when calculating the orbits of Pallas and Juno in 1805, 160 years before Cooley and Tukey found their similar Cooley–Tukey FFT algorithm. He developed it as a trigonometric interpolation method, but the paper Theoria Interpolationis Methodo Nova Tractata was published only posthumously in 1876, preceded by the first presentation by Joseph Fourier on the subject in 1807.