Home > freetb4matlab > linear-algebra > onenormest.m

onenormest

PURPOSE ^

%

SYNOPSIS ^

function [est, v, w, iter] = onenormest (varargin)

DESCRIPTION ^

% -*- texinfo -*-
% @deftypefn {Function File} {[@var{est}, @var{v}, @var{w}, @var{iter}] =} onenormest (@var{a}, @var{t}) 
% @deftypefnx {Function File} {[@var{est}, @var{v}, @var{w}, @var{iter}] =} onenormest (@var{apply}, @var{apply_t}, @var{n}, @var{t})
%
% Apply Higham and Tisseur's randomized block 1-norm estimator to
% matrix @var{a} using @var{t} test vectors.  If @var{t} exceeds 5, then
% only 5 test vectors are used.
%
% If the matrix is not explicit, e.g., when estimating the norm of 
% @code{inv (@var{A})} given an LU factorization, @code{onenormest} applies 
% @var{A} and its conjugate transpose through a pair of functions 
% @var{apply} and @var{apply_t}, respectively, to a dense matrix of size 
% @var{n} by @var{t}.  The implicit version requires an explicit dimension 
% @var{n}.
%
% Returns the norm estimate @var{est}, two vectors @var{v} and
% @var{w} related by norm
% @code{(@var{w}, 1) = @var{est} * norm (@var{v}, 1)},
% and the number of iterations @var{iter}.  The number of
% iterations is limited to 10 and is at least 2.
%
% 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{condest, norm, cond}
% @end deftypefn

CROSS-REFERENCE INFORMATION ^

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