Example of Bairstow Method

 

Bairstow’s Method Example: (Scilab syntax)

// f(x)=x^3-3*x^2+4*x-2 a3=1, a2=-3, a1=4, a0=-2 r(1)=1.5, s(1)=-2.5 tol1=10^-6, tol2=10^-6 //iter0 k=1  b3=a3  b2=a2+r(k)*b3  b1(k)=a1+r(k)*b2+s(k)*b3  b0(k)=a0+r(k)*b1(k)+s(k)*b2 c3=b3 c2=b2+r(k)*c3 c1=b1(k)+r(k)*c2+s(k)*c3 =!c2,c3"c1,c2#, =!c2,c3"c1, c2#, b=!-b1(k)"-b0(k) b=!-b1(k)"-b0(k)## $=%b &eltar=$(1) &eltas=$(2) //iter1 k=2 r(k)=r(k-1)+&eltar  s(k)=s(k-1)+&eltas  b3=a3  b2=a2+r(k)*b3  b1(k)=a1+r(k)*b2+s(k)*b3  b0(k)=a0+r(k)*b1(k)+s(k)*b2 c3=b3 c2=b2+r(k)*c3 c1=b1(k)+r(k)*c2+s(k)*c3

 

=!c2,c3"c1,c2#, b=!-b1(k)"-b0(k) =!c2,c3"c1,c2#, b=!-b1(k)"-b0(k)## $=%b &eltar=$(1) &eltas=$(2) 'ile (((abs(&eltar)tol1)(abs(&eltas)tol1))((abs(b1(k)-b1(k-1))tol2) (((abs(&eltar)tol1)(abs(&eltas)tol1))((abs(b1(k)-b1(k-1))tol2) (abs(b0(k)-b0(k-1))tol2))) //satisfi all stoi criteria   k=k+1   r(k)=r(k-1)+&eltar    s(k)=s(k-1)+&eltas   b3=a3 //actall, //actall, soe rocesses are re&&at, o ca eliiate te if o 'at   b2=a2+r(k)*b3   b1(k)=a1+r(k)*b2+s(k)*b3   b0(k)=a0+r(k)*b1(k)+s(k)*b2   c3=b3   c2=b2+r(k)*c3   c1=b1(k)+r(k)*c2+s(k)*c3   =!c2,c3"c1,c2#, =!c2,c3"c1,c2#, b=!-b1(k)"-b0(k)#   $=%b   &eltar=$(1)   &eltas=$(2) e&   &is(r(k),r=) &is(s(k),s=) &is(k-1, of iter=) s'er  r = 2 s = 2  of iter = 6 actor

 x

2

−2 x + 2

 

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