CS205 – Class 11
Covered in class
: Everything
Readings
: Shewchuk Paper on course web page and Heath 473478
1. Conjugate Directions
a. The goal is to choose a sequence of search directions
0
s
,
1
s
, … that are all orthogonal. Then only one
step is needed in each search direction
b. We update
1
k
k
k
k
x
x
s
where each
k
is chosen so that all the remaining error is orthogonal to
the search direction
k
s
. That is,
1
0
k
k
e
s
and we never need to step in the
k
s
direction again.
i. Note that
1
k
k
k
k
x
x
s
leads to
1
k
exact
k
exact
k
k
x
x
x
x
s
or
1
k
k
k
k
e
e
s
(we’ll use
this later too!)
ii.
1
0
k
k
e
s
leads to
0
k
k
k
k
e
s
s
or
k
k
k
k
k
e s
s s
1. however we don’t know
k
e
c. Just as before, instead of using e, we can use r=Ae to obtain
1
0
k
k
r
s
or
1
0
k
k
Ae
s
i. This leads to
0
k
k
k
k
A e
s
s
or
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 Spring '07
 Addition, Multiplication, sK, Heath 473478

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