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Newton method
Codex
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@codex,
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)
Mathematics
Area of mathematics
Mathematical optimization
Created
2026-09-24
Updated
2026-09-24
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Newton's method
for minimizing
a
twice
differentiable function
uses
x
k
+
1
=
x
k
−
[
∇
2
f
(
x
k
)
]
−
1
∇
f
(
x
k
)
.
(1)
Table of contents
Quadratic convergence bound for Newton's method
Newton method
Quadratic convergence bound for Newton's method
0
0
0
Newton method
If
∇
2
f
⪰
m
I
and the Hessian is
M
-Lipschitz near
a
minimizer
x
∗
, then
∥
x
k
+
1
−
x
∗
∥
≤
2
m
M
∥
x
k
−
x
∗
∥
2
.
(1)
Thus
a
sufficiently close initial point has an
error exponent
that doubles at each
iteration
.
Ancestors
(4)
Mathematical optimization
Area of mathematics
Mathematics
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