>> x=[1:6],y=x+1 x = [ 1 2 3 4 5 6 ] y = [ 2 3 4 5 6 7 ] >> polyfit(x,y,4) p = 5.1958E-14 -9.6634E-13 -2.4727E-12 1 1The coefficients

`p(1),p(2),p(3)`

should vanish since
`x`

and `y`

represent a perfect straight line.
This is an unstable problem, and it can be easily extended
to make Jasymca completely fail.
In our second attempt we use the Lapack-routine `linlstsq`

:
>> x=[1:6],y=x+1; >> l=length(x);n=4; >> X=(x'*ones(1,n+1)).^(ones(l,1)*(n:-1:0)) >> linlstsq(X,y') ans = -1.6288E-18 -7.0249E-17 1.0653E-15 1 1The coefficients

`p(1),p(2),p(3)`

are now significantly smaller.
This particular problem can be solved exactly using Jasymca-routines
and exact numbers, which avoids any rounding errors:
>> x=rat([1:6]);y=x+1; >> polyfit(x,y,4) p = 0 0 0 1 1

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2009-03-15