CS 361 Concurrent Programming
Assignment 1
Log into your queen UNIX account. Perform the following steps, starting out in your
home directory. The steps are numbered to help you keep track.
The goal of this programming assignment is to write your first Java program, if you have
not already done so.
mkdir asmt1
chmod 700 asmt1
cd asmt1
Write Java classes to integrate functions using “Adaptive Quadrature” method. Adaptive
quadrature is a numerical integration procedure in which the interval of integration is
recursively subdivided until an error tolerance is met for the approximate integral on each
subinterval. The error estimate for a given subinterval is based on the difference between
two different quadrature rules applied on the subinterval. The two quadrature rules used
in this module are the midpoint and trapezoid rules, and the recursion tree can be
traversed in depth-first or breadth-first order, or in any other order you may choose.
a. The midpoint method: evaluate the function at the midpoint of the interval and
multiply it by the width of the sub-interval.
b. The trapezoid method: evaluate the function at the ends of the internal and
compute the average of these 2 values. Multiply that average by the width of the
sub-interval.
Evaluate the midpoint rule, and trapezoid rule, for the current subinterval, as well as the
magnitude of their difference. If the two quadrature rules differ by less than the selected
tolerance, or if the subinterval width falls below some minimum allowed value [make it a
constant 10^(-5) in your program] , then that subinterval is declared "completed".
The number of subdivisions required to converge to within a given tolerance depends on
the nature of the integrand function. In particular, a region where the integrand function
has an abrupt change, sharp peak, cusp, or discontinuity will require many more
subdivisions (and hence function evaluations) than a region where the integrand function
is well behaved. The assigned integrand functions are listed in rough order of difficulty,
from easiest to hardest.
You will need to define an interface class Function with the following methods:
