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Math 581, Midterm 1. November 2, 2006
1. Suppose an approximation ^y to y = f(x) needs to be computed, where f(x)
is a scalar function of a scalar variable.
a) (7pt) Give the definition of the backward error for y = f(x).
b) (8pt) If f(x) =
, and our calculations for y = f(3) give ^y = 0.3. What is the
backward error involved in this calculation?
2. Using the backward error result for the vector inner product from Section 3.1
(formula (3.4)): for x, y Rn
y) = (x + x)T
y = xT
(y + y), |x| n|x|, |y| n|y|,
where |x| denotes the vector with elements |xi| and inequalities between vectors hold