Ariadne.jl

Arguments

• F!: F!(res, u, p) solves res = F(u) = 0
• u₀: Initial guess
• p: Parameters
• M: Length of the output of F!. Defaults to length(u₀)

Keyword Arguments

• tol_rel: Relative tolerance
• tol_abs: Absolute tolerance
• max_niter: Maximum number of iterations
• forcing: Maximum forcing term for inexact Newton. If nothing an exact Newton method is used.
• verbose:
• Workspace:
• M:
• N:
• krylov_kwarg
• callback:

Arguments

• F!: F!(res, u, p) solves res = F(u) = 0
• u: Initial guess
• p:
• res: Temporary for residual

Keyword Arguments

• tol_rel: Relative tolerance
• tol_abs: Absolute tolerance
• max_niter: Maximum number of iterations
• forcing: Maximum forcing term for inexact Newton. If nothing an exact Newton method is used.
• verbose:
• Workspace:
• M:
• N:
• krylov_kwarg
• callback:

newton_krylov(F, u₀::AbstractArray, M::Int = length(u₀); kwargs...)

Arguments

• F: res = F(u₀, p) solves res = F(u₀) = 0
• u₀: Initial guess
• p: Parameters
• M: Length of the output of F. Defaults to length(u₀).

Keyword Arguments

• tol_rel: Relative tolerance
• tol_abs: Absolute tolerance
• max_niter: Maximum number of iterations
• forcing: Maximum forcing term for inexact Newton. If nothing an exact Newton method is used.
• verbose:
• Workspace:
• M:
• N:
• krylov_kwarg
• callback:

Forcing

Implements forcing for inexact Newton-Krylov. The equation $‖F′(u)d + F(u)‖ <= η * ‖F(u)‖$ gives the inexact Newton termination criterion.

Implemented variants

• Fixed
• EisenstatWalker

Fixed(η = 0.1)

EisenstatWalker(η_max = 0.999, γ = 0.9)

JacobianOperator

Efficient implementation of J(f,x,p) * v and v * J(f, x,p)'

BatchedJacobianOperator{N}