help lopy

lopy.m not found.

help poly

 POLY Convert roots to polynomial.
    POLY(A), when A is an N by N matrix, is a row vector with
    N+1 elements which are the coefficients of the
    characteristic polynomial, DET(lambda*EYE(SIZE(A)) - A) .
 
    POLY(V), when V is a vector, is a vector whose elements are
    the coefficients of the polynomial whose roots are the
    elements of V . For vectors, ROOTS and POLY are inverse
    functions of each other, up to ordering, scaling, and
    roundoff error.
 
    ROOTS(POLY(1:20)) generates Wilkinson's famous example.
 
    See also ROOTS, CONV, RESIDUE, POLYVAL.

help polyval

 POLYVAL Evaluate polynomial.
    Y = POLYVAL(P,X), when P is a vector of length N+1 whose elements
    are the coefficients of a polynomial, is the value of the
    polynomial evaluated at X.
 
        Y = P(1)*X^N + P(2)*X^(N-1) + ... + P(N)*X + P(N+1)
 
    If X is a matrix or vector, the polynomial is evaluated at all
    points in X.  See also POLYVALM for evaluation in a matrix sense.
 
    Y = POLYVAL(P,X,[],MU) uses XHAT = (X-MU(1))/MU(2) in place of X.
    The centering and scaling parameters MU are optional output
    computed by POLYFIT.
 
    [Y,DELTA] = POLYVAL(P,X,S) or [Y,DELTA] = POLYVAL(P,X,S,MU) uses
    the optional output structure S provided by POLYFIT to generate
    error estimates, Y +/- delta.  If the errors in the data input to
    POLYFIT are independent normal with constant variance, Y +/- DELTA
    contains at least 50% of the predictions.
 
    See also POLYFIT, POLYVALM.

edit horner
fschange('C:\data\matlab\horner.m');
clear horner
P=[1,2,3]
P =
     1     2     3
polyval(P,4)
ans =
    27
horner(P,4)
??? Undefined function or variable 'n'.

Error in ==> C:\data\matlab\horner.m
On line 6  ==> for k=n:-1:0,

fschange('C:\data\matlab\horner.m');
clear horner
horner(P,4)
ans =
    24
fschange('C:\data\matlab\horner.m');
clear horner
horner(P,4)
ans =
    27
horner(P,10)
ans =
   123
polyval(P,10)
ans =
   123
edit naivep
fschange('C:\data\matlab\naivep.m');
clear naivep
naivep(P,10)
ans =
   123
fschange('C:\data\matlab\naivep.m');
clear naivep
uisave
fschange('C:\data\matlab\horner.m');
clear horner
P=[1,2,-3,4,-5]
P =
     1     2    -3     4    -5
naivep(P,10)
maxn =
     5
maxn =
    35
maxn =
   265
maxn =
        1735
maxn =
       11735
ans =
       11735
horner(P,10)
maxn =
     1
maxn =
    12
maxn =
   117
maxn =
        1174
maxn =
       11735
ans =
       11735
naivep(P,100)
maxn =
     5
maxn =
   395
maxn =
       29605
maxn =
     1970395
maxn =
   101970395
ans =
   101970395
horner(P,100)
maxn =
     1
maxn =
   102
maxn =
       10197
maxn =
     1019704
maxn =
   101970395
ans =
   101970395
P=[1,2,-3,40,-40,6,-7,8,-9]
P =
     1     2    -3    40   -40     6    -7     8    -9
horner(P,10)
maxn =
     1
maxn =
    12
maxn =
   117
maxn =
        1210
maxn =
       12060
maxn =
      120606
maxn =
     1206053
maxn =
    12060538
maxn =
   120605371
ans =
   120605371
naivep(P,10)
maxn =
     9
maxn =
    71
maxn =
   629
maxn =
        5371
maxn =
      394629
maxn =
     3605371
maxn =
     3605371
maxn =
    20605371
maxn =
   120605371
ans =
   120605371
roots(P)
ans =
  -4.7704          
   0.8839 + 2.7424i
   0.8839 - 2.7424i
   1.0320          
  -0.4452 + 0.5181i
  -0.4452 - 0.5181i
   0.4306 + 0.5353i
   0.4306 - 0.5353i
r=roots(P)
r =
  -4.7704          
   0.8839 + 2.7424i
   0.8839 - 2.7424i
   1.0320          
  -0.4452 + 0.5181i
  -0.4452 - 0.5181i
   0.4306 + 0.5353i
   0.4306 - 0.5353i
x=r(1)
x =
   -4.7704
naivep(P,x)
maxn =
     9
maxn =
   47.1629
maxn =
  206.4575
maxn =
  857.7946
maxn =
  2.1572e+004
maxn =
  1.2039e+005
maxn =
  1.5574e+005
maxn =
  2.6817e+005
maxn =
  2.6817e+005
ans =
 -2.3283e-010
horner(P,x)
maxn =
     1
maxn =
    2.7704
maxn =
   10.2156
maxn =
   10.2156
maxn =
   10.2156
maxn =
   10.2156
maxn =
   10.2156
maxn =
   10.2156
maxn =
   10.2156
ans =
 -2.3124e-010
diary off