Sparse Iterative Methods

Select a suitable iterative method to solve a system.

Overview

Sparse Iterative methods solve Ax = b through an iterative process that only requires multiplication by A or A. However, if A is numerically difficult, the iterative process may fail to converge to a solution. Further, even for problems where the process converges, it may do so slowly. Both of these issues can be fixed through the application of a problem-specific preconditioner that cheaply approximates the inverse of A.

Topics

Sparse Iterative Methods

func SparseConjugateGradient(SparseCGOptions) -> SparseIterativeMethod

Returns a conjugate gradient method with specified options.

struct SparseCGOptions

Options for creating a conjugate gradient method.

func SparseGMRES() -> SparseIterativeMethod

Returns a generalized minimal residual method.

func SparseGMRES(SparseGMRESOptions) -> SparseIterativeMethod

Returns a generalized minimal residual method with specified options.

struct SparseGMRESOptions

Options for creating a generalized minimal residual method.

func SparseLSMR() -> SparseIterativeMethod

Returns a default least squares minimum residual method.

func SparseLSMR(SparseLSMROptions) -> SparseIterativeMethod

Returns a least squares minimum residual method with specified options.

struct SparseLSMROptions

Options for creating a least squares minimum residual method.

Iterative Method Type

struct SparseIterativeMethod

Base type for all iterative methods.

See Also

Iterative Sparse Solving Methods

Implementing Iterative Methods

Use iterative methods to solve large problems faster and with a lower memory overhead than with direct methods.

Solving Systems Using Iterative Methods

Use iterative methods to solve systems of equations where the coefficient matrix is sparse.

Preconditioners

Create preconditioners for iterative solves.

Iterative Sparse Solve Functions

Solve a system using an iterative method.

Sparse Iterate Functions

Perform a single iteration of the specified iterative method.