Sparse Linear Systems

The solvers in this module focus on traditional least square problems for square or overdetermined linear systems \(A x = b\) where the matrix \(A\) is sparse and is represented by a linear operator abstraction providing the matrix multiplication and adjoint multiplication functions.

Solvers

lsqr(A, b, x0[, damp, atol, btol, conlim, …])	Solves the overdetermined system \(A x = b\) in least square sense using LSQR algorithm.
lsqr_jit(A, b, x0[, damp, atol, btol, …])	Solves the overdetermined system \(A x = b\) in least square sense using LSQR algorithm.
power_iterations(operator, b[, max_iters, …])	Computes the largest eigen value of a (symmetric) linear operator by power method
power_iterations_jit(operator, b[, …])	Computes the largest eigen value of a (symmetric) linear operator by power method
ista(operator, b, x0, step_size[, …])	Solves the problem \(\widehat{x} = \text{arg} \min_{x} \frac{1}{2}\| b - A x \|_2^2 + \lambda \mathbf{R}(x)\) via iterative shrinkage and thresholding.
ista_jit(operator, b, x0, step_size[, …])	Solves the problem \(\widehat{x} = \text{arg} \min_{x} \frac{1}{2}\| b - A x \|_2^2 + \lambda \mathbf{R}(x)\) via iterative shrinkage and thresholding.
fista(operator, b, x0, step_size[, …])	Solves the problem \(\widehat{x} = \text{arg} \min_{x} \frac{1}{2}\| b - A x \|_2^2 + \lambda \mathbf{R}(x)\) via fast iterative shrinkage and thresholding.
fista_jit(operator, b, x0, step_size[, …])	Solves the problem \(\widehat{x} = \text{arg} \min_{x} \frac{1}{2}\| b - A x \|_2^2 + \lambda \mathbf{R}(x)\) via fast iterative shrinkage and thresholding.

Data types

LSQRSolution	Solution for LSQR algorithm
PowerIterSolution	Solution of the eigen vector estimate
ISTAState	ISTA algorithm state
FISTAState	ISTA algorithm state