**Due March 8, 2005**

Topics for this problem set include round-off error and linear algebra.

- Write a program that uses the quadratic formula to compute both
roots of
in single precision. The program should also recompute the smaller
root from the larger, using the fact that the product of the roots
must equal 1 in this case. Explain any discrepancy. Which method
is preferable? What happens when you repeat this exercise in double
precision?
- As an example of an unstable algorithm, consider integer
powers of the ``Golden Mean'' . It can be
shown that , i.e. successively
higher powers of can be computed from a single subtraction
rather than a more expensive multiply. Write a single-precision
program to compute a table consisting of the columns ,
computed from the recursion relation, and computed directly
(i.e. ), for ranging from 1 to 20. Is
the round-off error random? What happens in double precision?
- Write a program to compute the instantaneous spin period of a
rigid body made up of identical, discrete, point particles. Use the
fact that the angular momentum is
1 *[For continuous bodies the summations are replaced by volume integrations and the particle masses become a mass density. In the present case the 's can be omitted entirely since the particles are identical.]*Write a program to solve Eq. (1) for (feel free to use the routines in*Numerical Recipes).**[On the department machines, look in*The spin period is then .`/local/src/lib/NumRecC/`for C or`NumRecF/`for FORTRAN.*Warning*: In C, remember*NR*'s funny array indexing convention...]- Test your code by reading the data file
http://www.astro.umd.edu/~dcr/Courses/ASTR415/ps2.dat

which is in the format (i.e. 6 values to a line separated by white space). The units are mks (SI). What is the spin period in hours? - Make a graphical representation of the body using your
favorite graphing package. If you use 2-D projections, be sure to
include enough viewing angles to get a complete picture.

- Test your code by reading the data file