Math 371 (Fall 2011): Midterm Exam
13 October 2011
Name
:
Q1
20 points
Q2
20 points
Q3
20 points
Q4
20 points
Q5
20 points
Total
100 points
1
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1. (20 points)
Answer each of the following questions briefly.
(a)
For scientific measurements, which of relative error and absolute error is
more important?
(b)
In double precision representation of floating point numbers, what is
β
(the base of the number system)? If the base of the double precision
floating point system is assumed to be
10
(which it is not), what is the
approximate value of
k
, the number of digits of precision?
(c)
Gaussian elimination with partial pivoting is faster than Gaussian elim
ination without partial pivoting. True or False?
(d)
On a typical modern laptop, it takes about a minute to solve a
1000
×
1000
linear system of the type
Ax
=
b
. True or False?
(e)
If a matrix can be multiplied with itself, it must be square.
True or
False?
(a)
Relative error. If we know that a quantity has been measured with 3%
accuracy we know something about the measurement.
On the other
hand, if we simply know that the absolute error in the measurement is
3 mm, we know virtually nothing about the quality of the measurement.
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 Fall '08
 KRASNY
 Math, Numerical Analysis, Quadratic equation, double precision, fixed point iteration

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