LSQR
Usage
#
IterativeSolvers.lsqr
— Function
lsqr(A, b; kwrags...) -> x, [history]
Same as lsqr!
, but allocates a solution vector x
initialized with zeros.
#
IterativeSolvers.lsqr!
— Function
lsqr!(x, A, b; kwargs...) -> x, [history]
Minimizes in the Euclidean norm. If multiple solutions exists returns the minimal norm solution.
The method is based on the Golub-Kahan bidiagonalization process. It is algebraically equivalent to applying CG to the normal equations but has better numerical properties, especially if A is ill-conditioned.
Arguments
-
x
: Initial guess, will be updated in-place; -
A
: linear operator; -
b
: right-hand side.
Keywords
-
damp::Number = 0
: damping parameter. -
atol::Number = 1e-6
,btol::Number = 1e-6
: stopping tolerances. If both are 1.0e-9 (say), the final residual norm should be accurate to about 9 digits. (The finalx
will usually have fewer correct digits, depending oncond(A)
and the size of damp). -
conlim::Number = 1e8
: stopping tolerance.lsmr
terminates if an estimate ofcond(A)
exceeds conlim. For compatible systems Ax = b, conlim could be as large as 1.0e+12 (say). For least-squares problems, conlim should be less than 1.0e+8. Maximum precision can be obtained by settingatol
=btol
=conlim
= zero, but the number of iterations may then be excessive. -
maxiter::Int = maximum(size(A))
: maximum number of iterations. -
verbose::Bool = false
: print method information. -
log::Bool = false
: output an extra element of typeConvergenceHistory
containing extra information of the method execution.
Return values
if log
is false
-
x
: approximated solution.
if log
is true
-
x
: approximated solution. -
ch
: convergence history.
ConvergenceHistory keys
-
:atol
=>::Real
: atol stopping tolerance. -
:btol
=>::Real
: btol stopping tolerance. -
:ctol
=>::Real
: ctol stopping tolerance. -
:anorm
=>::Real
: anorm. -
:rnorm
=>::Real
: rnorm. -
:cnorm
=>::Real
: cnorm. -
:resnom
=>::Vector
: residual norm at each iteration.
Implementation details
Adapted from: http://web.stanford.edu/group/SOL/software/lsqr/.