mundy::LanczosStrategy< Config, Precond > Class Template Reference

The Lanczos strategy: initialize/iterate/done/result over (Problem, State), preconditioned by Precond. More...

#include <eigenvalues.hpp>

Public Types
using	value_type = typename Config::value_type
using	config_t = Config
using	preconditioner_t = Precond
using	result_t = LanczosResult<value_type>

Public Member Functions
	LanczosStrategy (config_t cfg={})
	LanczosStrategy (config_t cfg, Precond &&precond)
const auto &	precond () const
template<class Problem, class State>
void	initialize (const Problem &prob, State &state) const
template<class Problem, class State>
bool	iterate (const Problem &prob, State &state) const
template<class State>
bool	done (const State &state) const
template<class State>
result_t	result (const State &state) const

Detailed Description

template<class Config, class Precond = NoPreconditioner>
class mundy::LanczosStrategy< Config, Precond >

For symmetric A (and SPD P), each iteration appends a row to T, whose extreme eigenvalues theta approach those of A (of P A) monotonically from inside. Each theta has the Ritz residual rho = ||A y - theta y|| of its Ritz vector y, within which an eigenvalue lies; by monotonicity, the least rho at an end so far still bounds it. The solve converges once that bound is at most tol |theta| at both ends.

Member Typedef Documentation

value_type

template<class Config, class Precond = NoPreconditioner>

using mundy::LanczosStrategy< Config, Precond >::value_type = typename Config::value_type

config_t

template<class Config, class Precond = NoPreconditioner>

using mundy::LanczosStrategy< Config, Precond >::config_t = Config

preconditioner_t

template<class Config, class Precond = NoPreconditioner>

using mundy::LanczosStrategy< Config, Precond >::preconditioner_t = Precond

result_t

template<class Config, class Precond = NoPreconditioner>

using mundy::LanczosStrategy< Config, Precond >::result_t = LanczosResult<value_type>

Constructor & Destructor Documentation

LanczosStrategy() [1/2]

template<class Config, class Precond = NoPreconditioner>

mundy::LanczosStrategy< Config, Precond >::LanczosStrategy ( config_t cfg = {} )

inlineexplicit

LanczosStrategy() [2/2]

template<class Config, class Precond = NoPreconditioner>

mundy::LanczosStrategy< Config, Precond >::LanczosStrategy ( config_t cfg, Precond && precond )

inline

Member Function Documentation

precond()

template<class Config, class Precond = NoPreconditioner>

const auto & mundy::LanczosStrategy< Config, Precond >::precond ( ) const

inline

initialize()

template<class Config, class Precond = NoPreconditioner>

template<class Problem, class State>

void mundy::LanczosStrategy< Config, Precond >::initialize ( const Problem & prob, State & state ) const

inline

iterate()

template<class Config, class Precond = NoPreconditioner>

template<class Problem, class State>

bool mundy::LanczosStrategy< Config, Precond >::iterate ( const Problem & prob, State & state ) const

inline

done()

template<class Config, class Precond = NoPreconditioner>

template<class State>

bool mundy::LanczosStrategy< Config, Precond >::done ( const State & state ) const

inline

result()

template<class Config, class Precond = NoPreconditioner>

template<class State>

result_t mundy::LanczosStrategy< Config, Precond >::result ( const State & state ) const

inline