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condest

PURPOSE ^

%

SYNOPSIS ^

function [est, v] = condest (varargin)

DESCRIPTION ^

% -*- texinfo -*-
% @deftypefn {Function File} {[@var{est}, @var{v}] =} condest (@var{a}, @var{t}) 
% @deftypefnx {Function File} {[@var{est}, @var{v}] =} condest (@var{a}, @var{solve}, @var{solve_t}, @var{t})
% @deftypefnx {Function File} {[@var{est}, @var{v}] =} condest (@var{apply}, @var{apply_t}, @var{solve}, @var{solve_t}, @var{n}, @var{t})
%
% Estimate the 1-norm condition number of a matrix @var{A}
% using @var{t} test vectors using a randomized 1-norm estimator.
% If @var{t} exceeds 5, then only 5 test vectors are used.
%
% If the matrix is not explicit, e.g., when estimating the condition 
% number of @var{a} given an LU factorization, @code{condest} uses the 
% following functions:
%
% @table @var
% @item apply
% @code{A*x} for a matrix @code{x} of size @var{n} by @var{t}.
% @item apply_t
% @code{A'*x} for a matrix @code{x} of size @var{n} by @var{t}.
% @item solve
% @code{A \ b} for a matrix @code{b} of size @var{n} by @var{t}.
% @item solve_t
% @code{A' \ b} for a matrix @code{b} of size @var{n} by @var{t}.
% @end table
%
% The implicit version requires an explicit dimension @var{n}.
%
% @code{condest} uses a randomized algorithm to approximate
% the 1-norms.
%
% @code{condest} returns the 1-norm condition estimate @var{est} and
% a vector @var{v} satisfying @code{norm (A*v, 1) == norm (A, 1) * norm
% (@var{v}, 1) / @var{est}}.  When @var{est} is large, @var{v} is an
% approximate null vector.
%
% References: 
% @itemize
% @item Nicholas J. Higham and Fran├žoise Tisseur, 'A Block Algorithm
% for Matrix 1-Norm Estimation, with an Application to 1-Norm
% Pseudospectra.' SIMAX vol 21, no 4, pp 1185-1201.
% @url{http://dx.doi.org/10.1137/S0895479899356080}
% @item Nicholas J. Higham and Fran├žoise Tisseur, 'A Block Algorithm
% for Matrix 1-Norm Estimation, with an Application to 1-Norm
% Pseudospectra.' @url{http://citeseer.ist.psu.edu/223007.html}
% @end itemize
%
% @seealso{norm, cond, onenormest}
% @end deftypefn

CROSS-REFERENCE INFORMATION ^

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