Newton’s Method: Square Systems
( )
0
f
x
Newton’s Algorithm
Select an initial vector
x
D Whil
(
i t
t
i
diti
h
t
d)
DoWhile (some appropriate stopping condition has not occurred)
Compute the Jacobian,
(
)
f
J
x
Let
y
solve the system of linear equations
(
)
(
)
f
J
x y
f
x
(assuming
(
)
f
J
x
is nonsingular)
x
x
y
End DoWhile
variable ,
'( )
0
function of one
f
x
Fact:
Assume
k
x
x
, and
(
)
f
J
x
is
nonsingular
(the
n
-dimensional analog of
'(
)
0
f
x
).
Then the rate of convergence is quadratic.
EE 103 Slides 7B2 (SEJ)
1

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