iterative Directory Reference

Abstractions and algorithms for iterative solvers. [tutorial] .

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Directory dependency graph for iterative:

Files
file	Action.h [code]
	Applies the "Action" of a linear operator, b := A*x, used in iterative solution algorithms.
file	ActionBase.h [code]
	Implementation detail, polymorphic base type contained/erased by Action.
file	AllActions.h [code]
	Blanket include for every Action type and all their composition functions (operator +,-,*, etc).
file	bicgstab.h [code]
	Linear system solution via bicgstab (for invertible action A)
file	bothcat.h [code]
	Routines to concatenate Action's in two-by-two fashion.
file	ConcatenateAction.h [code]
	An Action that concatenates other Action's, think horzcat() or vertcat().
file	diagcat.h [code]
	Routines to concatenate Action's in diagonal fashion.
file	DifferenceAction.h [code]
	Composes two Action's A and B, yielding an Action that applies (A-B)*X.
file	DimmAction.h [code]
	An Action for multiplying by a DiagonalMatrix using dimm()
file	fgmres.h [code]
	Linear system solution via (flexible) fgmres (for invertible action A)
file	GemmAction.h [code]
	An Action for multiplying by a dense Matrix or SparseMatrix using gemm().
file	gmres.h [code]
	Linear system solution via gmres (for invertible action A)
file	HemmAction.h [code]
	An Action for multiplying by a hermitian dense Matrix or SparseMatrix using hemm()
file	horzcat.h [code]
	Routines to concatenate Action's in left/right fashion.
file	ICholeskySolver.h [code]
	Incomplete Cholesky preconditioner. Presents a solve() function, but it's only approximate.
file	IdentityAction.h [code]
	An Action that is just the identity operator.
file	ILUSolver.h [code]
	Incomplete LU preconditioner. Presents a solve() function, but it's only approximate.
file	lanczos1.h [code]
	Finds one dominant eigenpair of a real symmetric Action.
file	lanczosn.h [code]
	Finds several dominant eigenpairs of a real symmetric Action.
file	lopcg1.h [code]
	Finds one small eigenpair of a real symmetric Action.
file	lopcgn.h [code]
	Finds several small eigenpairs of a real symmetric Action.
file	LowerAction.h [code]
	Routines for making double-precision Action's act like float-precision ones, accepting some loss of accuracy. Complementary to raise_precision()
file	minres.h [code]
	Linear system solution via minimum residual method (symmetric action A, can be indefinite)
file	mixed_refine.h [code]
	Like refine(), but uses a low-precision M to solve/refine a high-precision A.
file	MrhsReshaper.h [code]
	Implementation detail for iterative linear solvers that operate on multiple right hand sides (Mrhs).
file	NegateAction.h [code]
	Returns the negation of an Action A.
file	pcg.h [code]
	Linear system solution via conjugate gradients (symmetric positive definite action A)
file	power.h [code]
	Applies the power method to extract dominant eigenpair.
file	ProductAction.h [code]
	Composes two Action's A and B, yielding an Action that cascades A*(B*X)
file	RaiseAction.h [code]
	Routines for making float-precision Action's act like double-precision ones, accepting some loss of accuracy. Used in the context of backwards refinement or krylov solution that operates in mixed precision. (e.g. use a float- precision preconditioner to solve a double-precision forward operator)
file	refine.h [code]
	Generic algorithm for solving with backwards refinement, implemented in terms of Action's.
file	RefineAction.h [code]
	Adapts a class with a .refine() method into an Action.
file	ReshapeAction.h [code]
	Reshapes/clones an Action A into diag(A,A,A,..), used by "thick" iterative solvers to apply A to multiple contiguous column vectors.
file	ScaleAction.h [code]
	Scales an Action by a constant.
file	SolveAction.h [code]
	Adapts a class with a .solve() method into an Action.
file	stationary.h [code]
	Implementations of classical stationary iterations: jacobi(), seidel(), sor() and ssor()
file	SumAction.h [code]
	Composes two Action's A and B, yielding an Action that applies (A+B)*X.
file	SymmAction.h [code]
	An Action for multiplying by a symmetric dense Matrix. LowerMatrix or SparseMatrix using symm()
file	TrmmAction.h [code]
	An Action for multiplying by a triangular Matrix, LowerMatrix or SparseMatrix using trmm().
file	TrsmAction.h [code]
	An Action for solving by a triangular Matrix, LowerMatrix or SparseMatrix using trsm().
file	UserAction.h [code]
	Adapts user code (encapsulated in a class) into an Action.
file	vertcat.h [code]
	Routines to concatenate Action's in top/bottom fashion.
file	ZeroAction.h [code]
	An all-zero Action of specified size.

Detailed Description

Abstractions and algorithms for iterative solvers. [tutorial] .