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Map · 65

numerical analysis

MSC 65 · Numerical analysis

81 declarations (21 theorems, 60 definitions) across 2 files. 0 of the 3 famous theorems listed for this area are in Mathlib (0%).

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Subareas2

  • 65G Error analysis and interval analysis 69
  • 65D Numerical approximation and computational geometry (primarily algorithms) 12

Famous theorems0 of 3

From the 1000+ theorems project, which classifies each theorem by MSC area.

Not yet in Mathlib · 3

Undergraduate topics still missing34 of 36

From Mathlib's own undergraduate checklist.

Numerical Analysis · 34 of 36

  • Solving systems of linear inequalities › conditioning
  • Solving systems of linear inequalities › Gershgorin-Hadamard theorem
  • Solving systems of linear inequalities › Gauss’s pivot
  • Solving systems of linear inequalities › LU decomposition
  • Iterative methods › Jacobian
  • Iterative methods › Gauss-Seidel
  • Iterative methods › convergence analysis
  • Iterative methods › spectral ray
  • Iterative methods › singular value decomposition
  • Iterative methods › example of discretisation matrix by finite differences of the laplacian in one dimension
  • Iterative methods of solving systems of real and vector-valued equations › linear systems case
  • Iterative methods of solving systems of real and vector-valued equations › proper element search
  • Iterative methods of solving systems of real and vector-valued equations › brute force method
  • Iterative methods of solving systems of real and vector-valued equations › optimization of convex function in finite dimension
  • Iterative methods of solving systems of real and vector-valued equations › gradient descent square root
  • Iterative methods of solving systems of real and vector-valued equations › nonlinear problems with real and vector values
  • Iterative methods of solving systems of real and vector-valued equations › bisection method
  • Iterative methods of solving systems of real and vector-valued equations › Picard method
  • Iterative methods of solving systems of real and vector-valued equations › Newton’s method
  • Iterative methods of solving systems of real and vector-valued equations › rate of convergence and estimation of error
  • Numerical integration › Rectangle method
  • Numerical integration › error estimation
  • Numerical integration › Monte Carlo method
  • Numerical integration › rate of convergence
  • Numerical integration › application to the calculation of multiple integrals
  • Approximation of numerical functions › estimation of the error
  • Ordinary differential equations › numerical aspects of Cauchy's problem
  • Ordinary differential equations › explicit Euler method
  • Ordinary differential equations › consistency
  • Ordinary differential equations › stability
  • Ordinary differential equations › convergence
  • Ordinary differential equations › order
  • Fourier transform › discrete Fourier transform on a finite abelian group
  • Fourier transform › fast Fourier transform

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