Write a program, in the language of your preference, that computes roots for polynomials. The program should take as input a file which contains description of a polynomial in the following format. (Solved)
computer science
Description
Exercise 1
Write a program, in
the language of your preference, that computes roots for polynomials. The
program should take as input a file which contains description of a polynomial
in the following format:
n
a(n) a(n-1) a(n-2) ... a(2) a(1) b
where n is the degree of the polynomial, a(i) is the coefficient of the monomial of
degree i, and b is the constant term. For example, the
polynomial:
3x^3 + 5x^2 - 7
would be represented
as:
3
3 5 0 -7
The file should have
extension .pol, for example, fun1.pol would be a suitable name for a file. The
program should use bisection method by default and should place the solution in
a file with the same name as the input, but with extension .sol (such as
fun1.sol), with format:
root iterations outcome
where root is the last root approximation, iterations is the total number of iterations
performed by the algorithm, and outcome should be one of success if the algorithm reached convergence,
or fail if the algorithm
didn't converge.
For all algorithms,
the error tolerance should be IEEE 754 single precision. You should implement
the following algorithms:
·
Bisection method.
·
Newton's Method.
·
Secant Method.
·
Hybrid: starts with bisection for early iterations and switches
to newton's.
The program should use
bisection as default and operate as follows:
> polRoot [-newt, -sec] [-maxIt n]
initP [initP2] polyFileName
By default the program
uses bisection, but this can be modified with -newt for Newton's or -sec for
Secant. The program should attempt 10,000 iterations by default, but this can
be modified with -maxIter and the number of desired iterations. The initial
point is provided (or an extra point for bisection and secant). For example, to
run bisection method on file fun1.pol, with initial points 0 and 1:
> polRoot 0 1 fun1.pol
to run newton's with
initial point 0:
> polRoot -newt 0 fun1.pol
and to run secant,
with initial points 0 and 1, for 100,000 iterations:
> polRoot -sec -maxIter 100000 0 1 fun1.pol
Exercise 2
Use your program to
compute solutions for all polynomial functions depicted in the text of this
assignment.
