Sparse Iterative Methods

Overview

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

Topics

Sparse Iterative Methods for Symmetric Positive-Definite Coefficient Matrices

• SparseConjugateGradient()
• SparseConjugateGradient(_:)
• SparseCGOptions

Sparse Iterative Methods for Symmetric Indefinite and Unsymmetric Coefficient Matrices

• SparseGMRES()
• SparseGMRES(_:)
• SparseGMRESOptions

Sparse Iterative Methods for Overdetermined and Underdetermined Systems

• SparseLSMR()
• SparseLSMR(_:)
• SparseLSMROptions

Iterative Method Structure

• SparseIterativeMethod

See Also

Solving systems with iterative sparse methods

• Solving systems using iterative methods
• Sparse Iterative Solving Functions (Matrix RHS)
• Sparse Iterative Solving Functions (Vector RHS)
• Sparse Iterate Functions
• Preconditioners