List of numerical procedures

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The list of numerical methods lists methods of numerical mathematics according to application areas.

Systems of linear equations

Nonlinear systems of equations

Numerical integration

Approximation and interpolation


Numerics of ordinary differential equations

Numerics of partial differential equations

Calculation of eigenvalues

  • QR algorithm : Calculation of all eigenvalues, but associated with high costs.
  • LR algorithm : Also called stair iteration, forerunner of the QR method, but less reliable.
  • Power method: This allows the calculation of the greatest eigenvalue.
  • Subspace iteration : This is a multidimensional extension of the power method and allows the simultaneous calculation of several of the largest eigenvalues.
  • Inverse iteration : This allows the rapid calculation of eigenvalues ​​close to a shift.
  • Rayleigh quotient iteration : A special, very fast converging variant of the inverse iteration with shift.
  • Lanczos method : calculation of some eigenvalues ​​of large sparse matrices .
  • Arnoldi method : calculation of some eigenvalues ​​of large sparse matrices.
  • Jacobi method : calculation of all eigenvalues ​​and eigenvectors of small symmetrical matrices.
  • Jacobi-Davidson method : calculation of some eigenvalues ​​of large sparse matrices.
  • Folded Spectrum Method : Calculation of an eigenvalue and the associated eigenvector near a shift (from the center of the spectrum).