Contents

SparseLSMR(_:)

Returns a least squares minimum residual method with specified options.

Declaration

func SparseLSMR(_ options: SparseLSMROptions) -> SparseIterativeMethod

Parameters

  • options:

    The LSMR options to use when creating the LSMR method.

Return Value

A SparseIterativeMethod structure that represents a default LSMR method.

Discussion

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 AᵀAx = Aᵀb 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(_:). For square, full-rank unsymmetric or indefinite equations, use SparseGMRES(_:).

See Also

Sparse Iterative Methods for Overdetermined and Underdetermined Systems