Bairstow method (Method-2). Algorithm Formula : b_2=a_2-pb_1-qb

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Home > Numerical methods calculators > Bairstow method example

Bairstow method example ( Enter your problem )

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(Method-1). Algorithm Formula : $b_0=a_0+rb_1+sb_2$
(Method-1). Example-1 $f(x)=x^4-3x^3+3x^2-3x+2$ and $r=0.1,s=0.1$
(Method-1). Example-2 $f(x)=x^4-2x^3+6x^2-2x+5$ and $r=-1,s=-1$
(Method-2). Algorithm Formula : $b_2=a_2-pb_1-qb_0$
(Method-2). Example-1 $f(x)=x^3+x^2-x+2$ and $r=-0.9, s=0.9$
(Method-2). Example-2 $f(x)=x^4+x^3+2x^2+x+1$ and $r=0.5, s=0.5$

3. (Method-1). Example-2

$f(x)=x^4-2x^3+6x^2-2x+5$ and

$r=-1,s=-1$
(Previous example)

5. (Method-2). Example-1

$f(x)=x^3+x^2-x+2$ and

$r=-0.9, s=0.9$
(Next example)

4. (Method-2). Algorithm Formula : $b_2=a_2-pb_1-qb_0$

Algorithm

Bairstow method-2 Algorithm
Step-1:	Find coefficient from the equation $a_0x^n + a_1x^(n-1) + a_2x^(n-2) + ... + + a_nx^0$ Let initial approximation be $p_0,q_0$ $b_0 = a_0$ ; $c_0 = a_0$ ;
Step-2:	$b_i=a_i+p_0b_(i-1)+q_0b_(i-2)$
Step-3:	$c_i=b_i+p_0c_(i-1)+q_0c_(i-2)$
Step-4:	$Delta p=-(b_nc_(n-3)-b_(n-1)c_(n-2))/(c_(n-2)^2-c_(n-3)(c_(n-1)-b_(n-1)))$ $Delta q=-(b_(n-1)(c_(n-1)-b_(n-1))-b_nc_(n-2))/(c_(n-2)^2-c_(n-3)(c_(n-1)-b_(n-1)))$ $p_1=p_0+Delta p$ $q_1=q_0+Delta q$
Step-5:	if $\|p_1-p_0\| <= "Accuracy" "and" \|q_1-q_0\| <= "Accuracy"$ then answer are $p_1,q_1$ and stop the procedure else $p_0=p_1,q_0=q_1$ and goto step-2