Lab App 1.1 Exercise 1: Read the Bisection Algorithm handout (bisection.pdf) and

Question

Lab App 1.1 Exercise 1: Read the Bisection Algorithm handout (bisection.pdf) and write a function for the algorithm that returns the answer to the calculation. The main function is responsible for reading the input parameters and writing the output. Make sure to check input for errors before calling the Bisection algorithm. Use the algorithm with the given function in the example, which you will have to code into the program as a C++ function. Follow the example given.

Lab App 1.2 (Extra Credit) Gaussian Elimination with Backward Substitution Exercise 1 Read the Gaussian Elimination Algorithm handout (gaussian.pdf) and write the algorithm in a function called gaussian. The main function should read the input coefficients as user input (from console), call gaussian, and write the results to the console. The coefficients for the two dimensional array (matrix) A and the one dimensional array B should be read into the augmented array a[n][n+1], where the last column (a[i][n+1]) contains the B array. should be used to read the input coefficients and passed to the gaussian function. Follow the example given.

Explanation / Answer

package nisarg; import java.util.Scanner; public class BetterBisection { public static void main(String[] args) { double a, b, c; // a, b and c have the usual meaning double f_of_a, f_of_b; // f_of_a, f_of_b store values of f(a) and f(b) // respectively int highest_degree; System.out.println("What is the highest degree of your polynomial? "); Scanner input = new Scanner(System.in); highest_degree = input.nextInt(); for (int i = highest_degree; i >= 0; i--) { int coeff_deg_i; coeff_deg_i = poly_input(i); // System.out.println(coeff_deg_i); } // The following do-while loop keeps asking the user for a and b until // f(a)f(b) does not become negative do { a = input(); b = input(); if (f(a) * f(b) >= 0) { System.out .println("Sorry the two numbers are not bracketing the root. Please try again "); } } while (f(a) * f(b) >= 0); f_of_a = f(a); f_of_b = f(b); double root = bisectionMethod(f_of_a, f_of_b, a, b); System.out.println("Root is : " + root); } public static double input() { // Reads in the bracketing number i.e a and b Scanner input = new Scanner(System.in); System.out.println("Enter a bracketing number"); return (input.nextDouble()); } public static double f(double num) { // Calculates f(x) given x and returns // f(x) final int COEFF_DEG_3 = 1; // Coefficient of x^3 final int COEFF_DEG_2 = 4; // Coefficient of x^2 final int COEFF_DEG_0 = -10; // Coefficient of x^0 return (COEFF_DEG_3 * Math.pow(num, 3) + COEFF_DEG_2 * Math.pow(num, 2) + COEFF_DEG_0 * Math.pow(num, 0)); } public static double bisectionMethod(double f_of_a, double f_of_b, double a, double b) { // Does the actual work of evaluating double c; // the root using the method of bisection. double f_of_c; final double TOLERANCE = 0.0001; while (Math.abs(a - b) > TOLERANCE) { c = (a + b) / 2; f_of_c = f(c); if (f_of_c * f(a) == 0 || f_of_c * f(b) == 0) { return c; } else if (f_of_c * f(a) > 0) { a = c; } else { b = c; } } return (a + b) / 2; } public static int poly_input(int degree) { System.out.println("Please enter coefficient for degree " + degree); Scanner input = new Scanner(System.in); int coefficient; coefficient = input.nextInt(); return coefficient; } }

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