Mathematica 2.0 for MS-DOS 386/7 (June 21, 1991)
Copyright 1988-91 Wolfram Research, Inc.

In[1]:= <<na1.m

In[2]:= (p[x_] = Bernstein[f,x]) // Timing

                                           2            3            4
Out[2]= {1.49 Second, 4.50158 x - 7.55435 x  - 5.31215 x  + 11.8364 x  - 
 
               5            6             7             -15  8
>     2.64843 x  - 1.98702 x  + 0.722845 x  + 4.30341 10    x  - 
 
                 9                10
>     0.0143009 x  + 0.000533314 x  }

In[3]:= Plot[r[x],{x,a,b}]

Out[3]= -Graphics-

In[4]:= FindMax[r,0.8,1.2]

Out[4]= 0.531966

In[5]:= SecondNorm[r]

Out[5]= 0.371979

In[6]:= (p[x_] = Remes[f,x]) // Timing

                                                             2            3
Out[6]= {137.65 Second, 0.0000439682 + 4.99301 x + 0.183738 x  - 22.7144 x  +

               4            5            6            7            8
>     9.85334 x  - 3.92765 x  + 56.2714 x  - 81.9011 x  + 47.7346 x  - 
 
               9            10
>     12.7471 x  + 1.29514 x  }

In[7]:= Abs[r[0]]

Out[7]= 0.0000439682

In[8]:= SecondNorm[r]

Out[8]= 0.0000389243

In[9]:= (p[x_] = DiscreteMinSqr[f,x]) // Timing

                               -8                         2            3
Out[9]= {5. Second, 7.00341 10   + 4.97604 x + 0.471461 x  - 24.5876 x  +

               4            5            6            7            8
>     16.2527 x  - 16.8395 x  + 72.4605 x  - 94.6497 x  + 53.8646 x  - 
 
               9            10
>     14.3907 x  + 1.48336 x  }

In[10]:= Plot[r[x],{x,a,b}]

Out[10]= -Graphics-

In[11]:= FindMax[r,0,0.15]

Out[11]= 0.000407482

In[12]:= SecondNorm[r]

Out[12]= 0.000112959