RandomLinearAlgebraSolvers
Documentation for RandomLinearAlgebraSolvers.
RandomLinearAlgebraSolvers.RLAStoppingRandomLinearAlgebraSolvers.RandomVectorSketchRandomLinearAlgebraSolvers.RandomizedBlockKaczmarzRandomLinearAlgebraSolvers.RandomizedCDRandomLinearAlgebraSolvers.RandomizedCD2RandomLinearAlgebraSolvers.RandomizedKaczmarzRandomLinearAlgebraSolvers.RandomizedNewtonRandomLinearAlgebraSolvers.randomInvRandomLinearAlgebraSolvers.random_matrix_1RandomLinearAlgebraSolvers.random_matrix_2RandomLinearAlgebraSolvers.random_matrix_3RandomLinearAlgebraSolvers.random_matrix_4RandomLinearAlgebraSolvers.random_projector_rankRandomLinearAlgebraSolvers.random_projector_sparse
RandomLinearAlgebraSolvers.RLAStopping — Methodstp = RLAStopping(A, b::S; n_listofstates::Int = 0, kwargs...)Creator of a LAStopping tailored for this package. The problem, stp.pb, is a Stopping.LinearSystem if A is dense, and a LLSModels.LLSModel otherwise. The state allocates space for the residual, stp.current_state.res, of length |b|. This stopping uses the infinity norm of stp.current_state.res to declare optimality.
RandomLinearAlgebraSolvers.RandomVectorSketch — MethodRandom vector sketch
Section 3.2 in Gower, R. M., & Richtárik, P. (2015). Randomized iterative methods for linear systems. SIAM Journal on Matrix Analysis and Applications, 36(4), 1660-1690.
RandomLinearAlgebraSolvers.RandomizedBlockKaczmarz — MethodRandomized block Kaczmarz
Section 3.5 in Gower, R. M., & Richtárik, P. (2015). Randomized iterative methods for linear systems. SIAM Journal on Matrix Analysis and Applications, 36(4), 1660-1690.
RandomLinearAlgebraSolvers.RandomizedCD — MethodRandomized coordinate descent
Section 3.7 in Gower, R. M., & Richtárik, P. (2015). Randomized iterative methods for linear systems. SIAM Journal on Matrix Analysis and Applications, 36(4), 1660-1690.
RandomLinearAlgebraSolvers.RandomizedCD2 — MethodRandomized coordinate descent for symmetric positive definite matrix
Section 3.4 in Gower, R. M., & Richtárik, P. (2015). Randomized iterative methods for linear systems. SIAM Journal on Matrix Analysis and Applications, 36(4), 1660-1690.
RandomLinearAlgebraSolvers.RandomizedKaczmarz — MethodRandomized Kaczmarz
Section 3.3 in Gower, R. M., & Richtárik, P. (2015). Randomized iterative methods for linear systems. SIAM Journal on Matrix Analysis and Applications, 36(4), 1660-1690.
RK takes a step in the direction of the negative stochastic gradient. This means that it is equivalent to the SGD method. However, the stepsize choice is very special: RK chooses the stepsize which leads to the point which is closest to x* in the Euclidean norm.
RandomLinearAlgebraSolvers.RandomizedNewton — MethodRandomized Newton -> for symmetric positive definite matrix
Section 3.6 in Gower, R. M., & Richtárik, P. (2015). Randomized iterative methods for linear systems. SIAM Journal on Matrix Analysis and Applications, 36(4), 1660-1690.
RandomLinearAlgebraSolvers.randomInv — MethodSolve TAx=Tb with T a random projector
RandomLinearAlgebraSolvers.random_matrix_1 — MethodRandom projector of size k x m with a normal distribution
RandomLinearAlgebraSolvers.random_matrix_2 — MethodRandom projector of size k x m with -1 or 1 both with probability 1/2
RandomLinearAlgebraSolvers.random_matrix_3 — MethodRandom projector of size k x m with -1,0,1 respectively with probability 1/6,4/6,1/6
RandomLinearAlgebraSolvers.random_matrix_4 — MethodRandom projector of size k x m with orthogonal projection on a random k-dimensional linear subspace of R^m
RandomLinearAlgebraSolvers.random_projector_rank — MethodCheck the average rank of random projector over N random matrices of size k*m
RandomLinearAlgebraSolvers.random_projector_sparse — MethodCheck the average sparsity of random projector over N random matrices of size k*m