---
title: Sparse Iterative Methods
framework: accelerate
role: collectionGroup
role_heading: API Collection
path: accelerate/sparse-iterative-methods
---

# Sparse Iterative Methods

Select a suitable iterative method to solve a system.

## Overview

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()](accelerate/sparseconjugategradient().md)
- [SparseConjugateGradient(_:)](accelerate/sparseconjugategradient(_:).md)
- [SparseCGOptions](accelerate/sparsecgoptions.md)

### Sparse Iterative Methods for Symmetric Indefinite and Unsymmetric Coefficient Matrices

- [SparseGMRES()](accelerate/sparsegmres().md)
- [SparseGMRES(_:)](accelerate/sparsegmres(_:).md)
- [SparseGMRESOptions](accelerate/sparsegmresoptions.md)

### Sparse Iterative Methods for Overdetermined and Underdetermined Systems

- [SparseLSMR()](accelerate/sparselsmr().md)
- [SparseLSMR(_:)](accelerate/sparselsmr(_:).md)
- [SparseLSMROptions](accelerate/sparselsmroptions.md)

### Iterative Method Structure

- [SparseIterativeMethod](accelerate/sparseiterativemethod.md)

## See Also

### Solving systems with iterative sparse methods

- [Solving systems using iterative methods](accelerate/solving-systems-using-iterative-methods.md)
- [Sparse Iterative Solving Functions (Matrix RHS)](accelerate/sparse-iterative-solving-functions-matrix-rhs.md)
- [Sparse Iterative Solving Functions (Vector RHS)](accelerate/sparse-iterative-solving-functions-vector-rhs.md)
- [Sparse Iterate Functions](accelerate/sparse-iterate-functions.md)
- [Preconditioners](accelerate/preconditioners.md)