13-Nov-2013


1> edit horner.m


2> zeros(3,1)
ans =

   0
   0
   0



3> b = [1;2;3;4]
b =

   1
   2
   3
   4



4> b(2)
ans =  2


5> b(end)
ans =  4


6> b(:)
ans =

   1
   2
   3
   4



7> b(1:2)
ans =

   1
   2



8> A = [1 2 3; 4 5 6]
A =

   1   2   3
   4   5   6



9> A(:,2)
ans =

   2
   5



10> A(1:2,2)
ans =

   2
   5



11> A(2,:)
ans =

   4   5   6



12> A
A =

   1   2   3
   4   5   6



13> A(2,1)
ans =  4


14> help horner
'horner' is a function from the file C:\cygwin\home\achilles\programmi_matlab/Programmi_CS4a\horner.m

HORNER Metodo di Horner
   Y=HORNER(A,Z) calcola
     Y = A(1)*Z^N + A(2)*Z^(N-1) + ...
                             + A(N)*Z + A(N+1)
   con il metodo di divisione sintetica di Horner.

Additional help for built-in functions and operators is
available in the online version of the manual.  Use the command
'doc <topic>' to search the manual index.

Help and information about Octave is also available on the WWW
at http://www.octave.org and via the help@octave.org
mailing list.


15> a = [5 -1 7 -4];


16> horner(a)
error: 'z' undefined near line 12 column 23
error: called from:
error:   C:\cygwin\home\achilles\programmi_matlab/Programmi_CS4a\horner.m at line 12, column 9


16> horner(a, 3)
ans =  143


17> help polyval
'polyval' is a function from the file C:\Octave\Octave3.6.4_gcc4.6.2\share\octave\3.6.4\m\polynomial\polyval.m

 -- Function File: Y = polyval (P, X)

 -- Function File: Y = polyval (P, X, [], MU)

     Evaluate the polynomial P at the specified values of X.  When MU

     is present, evaluate the polynomial for (X-MU(1))/MU(2).  If X is

     a vector or matrix, the polynomial is evaluated for each of the

     elements of X.



 -- Function File: [Y, DY] = polyval (P, X, S)

 -- Function File: [Y, DY] = polyval (P, X, S, MU)

     In addition to evaluating the polynomial, the second output

     represents the prediction interval, Y +/- DY, which contains at

     least 50% of the future predictions.  To calculate the prediction

     interval, the structured variable S, originating from `polyfit',

     must be supplied.



     See also: polyvalm, polyaffine, polyfit, roots, poly






Additional help for built-in functions and operators is
available in the online version of the manual.  Use the command
'doc <topic>' to search the manual index.

Help and information about Octave is also available on the WWW
at http://www.octave.org and via the help@octave.org
mailing list.


18> polyval(a, 3)
ans =  143


19> [y, b] = horner(a, 3)
y =  143
b =

    5
   14
   49



20> conv(b, [1 -3])
ans =

     5
    -1
     7
  -147



21> a
a =

   5  -1   7  -4



22> conv(b, [1 -3]) + [0 0 0 143]
ans =

     5     5     5   148
    -1    -1    -1   142
     7     7     7   150
  -147  -147  -147    -4



23> conv(b, [1 -3])
ans =

     5
    -1
     7
  -147



24> conv(b, [1 -3]) + [0 0 0 143]'
ans =

   5
  -1
   7
  -4



25> conv(b, [1 -3]) + 143
ans =

   148
   142
   150
    -4



26> p = [1 -6 11 -6]
p =

    1   -6   11   -6



27> [radici, iter] = newtonhorner(p, 4)
radici =

   3.00000
   2.00000
   1.00000

iter =

   6
   6
   2



28> [radici, iter] = newtonhorner(p, 0)
radici =

   1.00000
   2.00000
   3.00000

iter =

   6
   6
   2



29> quit