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# SparseLSMROptions

Options for creating a least squares minimum residual method.

```
struct SparseLSMROptions
```

## Overview

LSMR is a minimal residual (MINRES) method for solving least squares. Use LSMR to solve equations of the form *Ax = b* where an exact solution doesn’t exist. The returned solution minimizes ‖ *b-Ax* ‖₂.

Although LSMR is equivalent to applying MINRES to the normal equations *A__ᵀ__Ax = A__ᵀ__b* in exact arithmetic, it has superior numerical behavior and is the preferred method. Due to the implicit squaring of the condition of *A* in the normal equations, LSMR may struggle to converge in single precision. Use double-precision arithmetic where possible.

For symmetric positive-definite systems, use [`SparseConjugateGradient(_:)`](/documentation/Accelerate/SparseConjugateGradient(_:)). For square, full-rank unsymmetric or indefinite equations, use [`SparseGMRES(_:)`](/documentation/Accelerate/SparseGMRES(_:)).

## Topics

### Initializers

[`init()`](/documentation/Accelerate/SparseLSMROptions/init())

Returns a new LSMR options structure.

[`init(reportError:lambda:nvec:convergenceTest:atol:rtol:btol:conditionLimit:maxIterations:reportStatus:)`](/documentation/Accelerate/SparseLSMROptions/init(reportError:lambda:nvec:convergenceTest:atol:rtol:btol:conditionLimit:maxIterations:reportStatus:))

Returns a new LSMR options structure using the specified parameters.

### Inspecting LSMR Options

[`atol`](/documentation/Accelerate/SparseLSMROptions/atol)

The absolute tolerance (default test) or *A* tolerance (Fong-Saunders test).

[`btol`](/documentation/Accelerate/SparseLSMROptions/btol)

The *B* tolerance (Fong-Saunders test only).

[`conditionLimit`](/documentation/Accelerate/SparseLSMROptions/conditionLimit)

The condition number limit (Fong-Saunders test only).

[`convergenceTest`](/documentation/Accelerate/SparseLSMROptions/convergenceTest)

The convergence test to use for iterative solve methods.

[`SparseLSMRConvergenceTest_t`](/documentation/Accelerate/SparseLSMRConvergenceTest_t)

Constants that specify the type of convergence test.

[`lambda`](/documentation/Accelerate/SparseLSMROptions/lambda)

The damping parameter lambda for regularized least squares.

[`maxIterations`](/documentation/Accelerate/SparseLSMROptions/maxIterations)

The maximum number of iterations.

[`nvec`](/documentation/Accelerate/SparseLSMROptions/nvec)

The number of vectors to use for local reorthogonalization.

[`reportError`](/documentation/Accelerate/SparseLSMROptions/reportError)

An optional error-reporting routine.

[`reportStatus`](/documentation/Accelerate/SparseLSMROptions/reportStatus)

An optional status-reporting routine.

[`rtol`](/documentation/Accelerate/SparseLSMROptions/rtol)

The relative convergence tolerance (default test only).


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