CS205 Practice Midterm #1
Multiple choice questions [7pts]
1. What can you say about a least squares solution?
(a) It satisfies
Ax
=
b
(b) It is given by the solution to the linear system
A
T
Ax
=
A
T
x
(c) It cannot be computed by the normal equations.
(d) The corresponding residual lies in the nullspace of
A
T
(e) It can be solved by performing a QR transformation with House
holder.
2. For which of the following reasons do iterative methods typically use the
residual to measure convergence? [1pt, circle all that apply]
(a) Absolute error is difficult to compute directly.
(b) Relative error does not indicate closeness to the solution.
(c) The residual will be zero if the current iterate is a solution.
(d) Using the residual is equivalent to using the absolute error.
3. Which of the following are true about condition numbers?
(a) The choice of
b
affects the condition number of
Ax
=
b
(b) A problem is poorly conditioned if its condition number is near zero
(c) If the condition number is negative the determinant of the matrix
is also negative.
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 Fall '07
 Fedkiw
 Linear Algebra, singular values, condition number

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