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Computer Arithmetic and Validity
book

Computer Arithmetic and Validity

by Ulrich Kulisch
April 2013
Intermediate to advanced content levelIntermediate to advanced
456 pages
16h 7m
English
De Gruyter
Content preview from Computer Arithmetic and Validity
Section 9.3 The interval Newton method 329
Automatic differentiation develops its full power in differentiable functions of sev-
eral real variables. For instance, values or enclosures of the gradient
gradf D
@f
@x
1
,
@f
@x
2
, :::,
@f
@x
n
of a function f : R
n
! R or the Jacobian or Hessian matrix can be computed directly
from the expression for the function f . No formal expressions for the derivatives are
needed. A special mode, the so-called reverse mode, allows a considerable acceler-
ation for many algorithms of automatic differentiation. In the particular case of the
computation of the gradient the following inequality can be shown to hold:
A.f ,
5
f/ ...
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Publisher Resources

ISBN: 9783110301731