The Matrix Function Toolbox: mft_tolerance(A) - File Exchange

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Highlights from
The Matrix Function Toolbox

arnoldi(A,q1,m) ARNOLDI Arnoldi iteration
ascent_seq(A) ASCENT_SEQ Ascent sequence for square (singular) matrix.
cosm(A) COSM Matrix cosine by double angle algorithm.
cosm_pade(A,m,sq) COSM_PADE Evaluate Pade approximation to the matrix cosine.
cosmsinm(A) COSMSINM Matrix cosine and sine by double angle algorithm.
cosmsinm_pade(A,m) COSMSINM_PADE Evaluate Pade approximations to matrix cosine and sine.
expm_cond(A) EXPM_COND Relative condition number of matrix exponential.
expm_frechet_pade(A,E,k) EXPM_FRECHET_PADE Frechet derivative of matrix exponential via Pade approx.
expm_frechet_quad(A,E,theta,r... EXPM_FRECHET_QUAD Frechet derivative of matrix exponential via quadrature.
fab_arnoldi(A,b,fun,m) FAB_ARNOLDI f(A)*b approximated by Arnoldi method.
funm_condest1(A,fun,fun_frech... FUNM_CONDEST1 Estimate of 1-norm condition number of matrix function.
funm_condest_fro(A,fun,fun_fr... FUNM_CONDEST_FRO Estimate of Frobenius norm condition number of matrix function.
funm_ev(A,fun) FUNM_EV Evaluate general matrix function via eigensystem.
funm_simple(A,fun) FUNM_SIMPLE Simplified Schur-Parlett method for function of a matrix.
logm_cond(A) LOGM_COND Relative condition number of matrix logarithm.
logm_frechet_pade(A,E) LOGM_FRECHET_PADE Frechet derivative of matrix logarithm via Pade approx.
logm_iss(A) LOGM_ISS Matrix logarithm by inverse scaling and squaring method.
logm_pade_pf(A,m) LOGM_PADE_PF Evaluate Pade approximant to matrix log by partial fractions.
mft_test(n) MFT_TEST Test the Matrix Function Toolbox.
mft_tolerance(A) MFT_TOLERANCE Convergence tolerance for matrix iterations.
polar_newton(A) POLAR_NEWTON Polar decomposition by scaled Newton iteration.
polar_svd(A) POLAR_SVD Canonical polar decomposition via singular value decomposition.
polyvalm_ps(c,A,s) POLYVALM_PS Evaluate polynomial at matrix argument by Paterson-Stockmeyer alg.
power_binary(A,m) POWER_BINARY Power of matrix by binary powering (repeated squaring).
quasitriang_struct(R) QUASITRIANG_STRUCT Block structure of upper quasitriangular matrix.
riccati_xaxb(A,B) RICCATI_XAXB Solve Riccati equation XAX = B in positive definite matrices.
rootpm_newton(A,p,c) ROOTPM_NEWTON Coupled Newton iteration for matrix pth root.
rootpm_real(A,p) ROOTPM_REAL Pth root of real matrix via real Schur form.
rootpm_schur_newton(A,p) ROOTPM_SCHUR_NEWTON Matrix pth root by Schur-Newton method.
rootpm_sign(A,p) ROOTPM_SIGN Matrix Pth root via matrix sign function.
signm(A) SIGNM Matrix sign decomposition.
signm_newton(A,scal) SIGNM_NEWTON Matrix sign function by Newton iteration.
sqrtm_db(A,scale) SQRTM_DB Matrix square root by Denman-Beavers iteration.
sqrtm_dbp(A,scale) SQRTM_DBP Matrix square root by product form of Denman-Beavers iteration.
sqrtm_newton(A,scal,maxit) SQRTM_NEWTON Matrix square root by Newton iteration (unstable).
sqrtm_newton_full(A, X0) SQRTM_NEWTON_FULL Matrix square root by full Newton method.
sqrtm_pd(A) SQRTM_PD Square root of positive definite matrix via polar decomposition.
sqrtm_pulay(A,D) SQRTM_PULAY Matrix square root by Pulay iteration.
sqrtm_real(A) SQRTM_REAL Square root of real matrix by real Schur method.
sqrtm_triang_min_norm(T) SQRTM_TRIANG_MIN_NORM Estimated min norm square root of triangular matrix.
sylvsol(A,B,C) SYLVSOL Solve Sylvester equation.
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from The Matrix Function Toolbox by Nick Higham
A MATLAB toolbox connected with functions of matrices.

mft_tolerance(A)

function tol = mft_tolerance(A)
%MFT_TOLERANCE   Convergence tolerance for matrix iterations.
%   TOL = MFT_TOLERANCE(A) returns a convergence tolerance to use in
%   the matrix iterations in the Matrix Function Toolbox applied to the
%   matrix A.  All functions in the toolbox call this function to set
%   the convergence tolerance.

tol = sqrt(length(A))*eps/2;

Highlights from The Matrix Function Toolbox

Highlights from
The Matrix Function Toolbox