3.6. Newton's Methad
Goal: Approdtimente solutions of fess=0
Example:
(03x-x=0
Over sendered algebraic tools do not help us solve this equation
Step Oi %o (Not the solution bust
close)
Step 1: Tangent like of f at x=xs
y= f(x) + f'(x) (x-x)
0 = f ( x ) + f ( x ₂ ) ( x − x ₁)
Find the rest of this line
f(xo)
=
step
2;
foxs
x = x² -
f(x₁)
Step H: XAH = Xu
f(x)
་
'f'(xn)
xd
(example: cos(x)-x=0
fcxs
il show equation has a solution
f(x)= cos(x)-x is continuous
Iterative formata for +(0)= | | f(1) =0-1/2 = -1
Newton's Method
There must be some some value of
where as=c in (0, 1)
fi fl
Goal: Approdtimente solutions of fess=0
Example:
(03x-x=0
Over sendered algebraic tools do not help us solve this equation
Step Oi %o (Not the solution bust
close)
Step 1: Tangent like of f at x=xs
y= f(x) + f'(x) (x-x)
0 = f ( x ) + f ( x ₂ ) ( x − x ₁)
Find the rest of this line
f(xo)
=
step
2;
foxs
x = x² -
f(x₁)
Step H: XAH = Xu
f(x)
་
'f'(xn)
xd
(example: cos(x)-x=0
fcxs
il show equation has a solution
f(x)= cos(x)-x is continuous
Iterative formata for +(0)= | | f(1) =0-1/2 = -1
Newton's Method
There must be some some value of
where as=c in (0, 1)
fi fl
