Deterministic and randomized, row-action and column-action  solvers have become increasingly popular owing to their simplicity, low computational and memory complexities, and ease of composition with other techniques. Indeed, such solvers can be highly tailored to the given problem structure and to the hardware platform on which the problem will be solved. However, whether such tailored solvers will converge to a solution is unclear. In this work, we provide a general set of assumptions under which such  solvers are guaranteed to converge with probability one  . As a result, we can provide practitioners with guidance on how to design highly tailored solvers that are also guaranteed to converge.
Deterministic and randomized, row-action and column-action linear solvers have become increasingly popular owing to their simplicity, low computational and memory complexities, and ease of composition with other techniques. Moreover, in order to achieve high-performance, such solvers must often be adapted to the given problem structure and to the hardware platform on which the problem will be solved. Unfortunately, determining whether such adapted solvers will converge to a solution has required equally unique analyses. As a result, adapted, reliable solvers are slow to be developed and deployed. In this work, we provide a general set of assumptions under which such adapted solvers are guaranteed to converge with probability one , and provide worst case rates of convergence . As a result, we can provide practitioners with guidance on how to design highly adapted, randomized or deterministic, row-action or column-action linear solvers that are also guaranteed to converge.
A
linear
R
Indeed, such solvers can be highly tailored
Moreover, in order to achieve high-performance, such solvers must often be adapted
R
However, whether such tailored
Unfortunately, determining whether such adapted
R
is unclear.
has required equally unique analyses. As a result, adapted, reliable solvers are slow to be developed and deployed.
A
adapted
A
, and provide worst case rates of convergence
R
tailored
adapted, randomized or deterministic, row-action or column-action linear