tstar=40

tstar =

    40

40/500

ans =

    0.0800

40/2500

ans =

    0.0160

1/50

ans =

    0.0200

% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

stiff
40/2500

ans =

    0.0160

2/100

ans =

    0.0200

40/2400

ans =

    0.0167

40/2300

ans =

    0.0174

40/2200

ans =

    0.0182

40/2100

ans =

    0.0190

40/2000

ans =

    0.0200

2/100

ans =

    0.0200

% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

Lstability
clear all
close all
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

Lstability
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

Lstability
% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

Lstability
A=rand(4)

A =

    0.8147    0.6324    0.9575    0.9572
    0.9058    0.0975    0.9649    0.4854
    0.1270    0.2785    0.1576    0.8003
    0.9134    0.5469    0.9706    0.1419

expm(A)

ans =

    4.7204    2.4561    4.1836    3.6737
    2.9289    2.4812    3.2288    2.5767
    1.4100    1.0458    2.5691    1.8036
    3.0394    1.9091    3.3480    3.3748

help log2
 LOG2   Base 2 logarithm and dissect floating point number.
    Y = LOG2(X) is the base 2 logarithm of the elements of X.
 
    [F,E] = LOG2(X) for each element of the real array X, returns an
    array F of real numbers, usually in the range 0.5 <= abs(F) < 1,
    and an array E of integers, so that X = F .* 2.^E.  Any zeros in X
    produce F = 0 and E = 0.  This corresponds to the ANSI C function
    frexp() and the IEEE floating point standard function logb().
 
    See also <a href="matlab:help log">log</a>, <a href="matlab:help log10">log10</a>, <a href="matlab:help pow2">pow2</a>, <a href="matlab:help nextpow2">nextpow2</a>, <a href="matlab:help realmax">realmax</a>, <a href="matlab:help realmin">realmin</a>.

    Overloaded methods:
       <a href="matlab:help sym/log2">sym/log2</a>

    Reference page in Help browser
       <a href="matlab:doc log2">doc log2</a>

2^1024

ans =

   Inf

2^1023

ans =

  8.9885e+307

[f,e]=log2(4.5)

f =

    0.5625


e =

     3

f*2^e

ans =

    4.5000

x=4.5

x =

    4.5000

x/(2^e)

ans =

    0.5625

x/(2^(e+1))

ans =

    0.2812

log2(x)

ans =

    2.1699

ceil(log2(x))+1

ans =

     4

A=toeplitz([-2,1,0,0,0])

A =

    -2     1     0     0     0
     1    -2     1     0     0
     0     1    -2     1     0
     0     0     1    -2     1
     0     0     0     1    -2

expm(A)

ans =

  Columns 1 through 4

    0.2153    0.1865    0.0864    0.0274
    0.1865    0.3016    0.2139    0.0928
    0.0864    0.2139    0.3081    0.2139
    0.0274    0.0928    0.2139    0.3016
    0.0064    0.0274    0.0864    0.1865

  Column 5

    0.0064
    0.0274
    0.0864
    0.1865
    0.2153

A=rand(4)

A =

    0.4218    0.6557    0.6787    0.6555
    0.9157    0.0357    0.7577    0.1712
    0.7922    0.8491    0.7431    0.7060
    0.9595    0.9340    0.3922    0.0318

phi1m(A)

ans =

    1.8552    0.8374    0.8887    0.6703
    0.9369    1.4742    0.8366    0.4304
    1.2005    1.0655    2.0763    0.8007
    1.0448    0.8910    0.7391    1.3728

phi1m(1)

ans =

    1.7183

exp(1)-1

ans =

    1.7183

a=rand(1)

a =

    0.2769

phi1m(a)

ans =

    1.1522

(exp(a)-1)/a

ans =

    1.1522

phi1m(A)

ans =

    1.8552    0.8374    0.8887    0.6703
    0.9369    1.4742    0.8366    0.4304
    1.2005    1.0655    2.0763    0.8007
    1.0448    0.8910    0.7391    1.3728

A\(expm(A)-eye(4))

ans =

    1.8552    0.8374    0.8887    0.6703
    0.9369    1.4742    0.8366    0.4304
    1.2005    1.0655    2.0763    0.8007
    1.0448    0.8910    0.7391    1.3728

A=[1,2,3;4,5,6;7,8,9]

A =

     1     2     3
     4     5     6
     7     8     9

det(A)

ans =

     0

phi1m(A)

ans =

   1.0e+05 *

    0.6943    0.8530    1.0118
    1.5722    1.9318    2.2914
    2.4501    3.0105    3.5709

A\(expm(A)-eye(3))
Warning: Matrix is close to singular or badly
scaled.
         Results may be inaccurate. RCOND =
         1.541976e-18.

ans =

   1.0e+07 *

   -1.0137   -1.1226   -1.1266
    2.0570    2.2815    2.2963
   -0.9961   -1.1010   -1.1010

% Modify expression to add input arguments.
% Example:
%   a = [1 2 3; 4 5 6]; 
%   foo(a);

stiff
diary off