Newton–Krylov method
Newton–Krylov methods are numerical methods for solving non-linear problems using Krylov subspace linear solvers.[1][2]
The Newton method, when generalised to systems of multiple variables, includes the inverse of a Jacobian matrix in the iteration formula. Calculation of the inverse of the Jacobian matrix is bypassed by employing a Krylov subspace method, e.g. the Generalized minimal residual method (GMRES), to solve the iteration formula.
References[]
- ^ Knoll, D.A.; Keyes, D.E. (2004). "Jacobian-free Newton–Krylov methods: a survey of approaches and applications". Journal of Computational Physics. 193 (2): 357. CiteSeerX 10.1.1.636.3743. doi:10.1016/j.jcp.2003.08.010.
- ^ Kelley, C.T. (2003). Solving nonlinear equations with Newton's method (1 ed.). SIAM.
External links[]
- Open Source code for MATLAB and Fortran90 with details on equations. [1]
Categories:
- Numerical analysis
- Applied mathematics stubs