This is a Java Program to Implement Gaussian Elimination Algorithm. Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.
Here is the source code of the Java Program to Implement Gaussian Elimination Algorithm. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.
/** ** Java Program to Implement Gaussian Elimination Algorithm **/ import java.util.Scanner; /** Class GaussianElimination **/ public class GaussianElimination { public void solve(double[][] A, double[] B) { int N = B.length; for (int k = 0; k < N; k++) { /** find pivot row **/ int max = k; for (int i = k + 1; i < N; i++) if (Math.abs(A[i][k]) > Math.abs(A[max][k])) max = i; /** swap row in A matrix **/ double[] temp = A[k]; A[k] = A[max]; A[max] = temp; /** swap corresponding values in constants matrix **/ double t = B[k]; B[k] = B[max]; B[max] = t; /** pivot within A and B **/ for (int i = k + 1; i < N; i++) { double factor = A[i][k] / A[k][k]; B[i] -= factor * B[k]; for (int j = k; j < N; j++) A[i][j] -= factor * A[k][j]; } } /** Print row echelon form **/ printRowEchelonForm(A, B); /** back substitution **/ double[] solution = new double[N]; for (int i = N - 1; i >= 0; i--) { double sum = 0.0; for (int j = i + 1; j < N; j++) sum += A[i][j] * solution[j]; solution[i] = (B[i] - sum) / A[i][i]; } /** Print solution **/ printSolution(solution); } /** function to print in row echleon form **/ public void printRowEchelonForm(double[][] A, double[] B) { int N = B.length; System.out.println("\nRow Echelon form : "); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) System.out.printf("%.3f ", A[i][j]); System.out.printf("| %.3f\n", B[i]); } System.out.println(); } /** function to print solution **/ public void printSolution(double[] sol) { int N = sol.length; System.out.println("\nSolution : "); for (int i = 0; i < N; i++) System.out.printf("%.3f ", sol[i]); System.out.println(); } /** Main function **/ public static void main (String[] args) { Scanner scan = new Scanner(System.in); System.out.println("Gaussian Elimination Algorithm Test\n"); /** Make an object of GaussianElimination class **/ GaussianElimination ge = new GaussianElimination(); System.out.println("\nEnter number of variables"); int N = scan.nextInt(); double[] B = new double[N]; double[][] A = new double[N][N]; System.out.println("\nEnter "+ N +" equations coefficients "); for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) A[i][j] = scan.nextDouble(); System.out.println("\nEnter "+ N +" solutions"); for (int i = 0; i < N; i++) B[i] = scan.nextDouble(); ge.solve(A,B); } }
Output:
Gaussian Elimination Algorithm Test Enter number of variables 3 Enter 3 equations coefficients 2 1 -1 -3 -1 2 -2 1 2 Enter 3 solutions 8 -11 -3 Row Echelon form : -3.000 -1.000 2.000 | -11.000 0.000 1.667 0.667 | 4.333 0.000 0.000 0.200 | -0.200 Solution : 2.000 3.000 -1.000
Related posts:
Mix plain text and HTML content in a mail
Java Program to Compute the Area of a Triangle Using Determinants
A Guide to Java SynchronousQueue
Spring Data Reactive Repositories with MongoDB
Send email with JavaMail
Changing Annotation Parameters At Runtime
Java Program to Find the Connected Components of an UnDirected Graph
Handling Errors in Spring WebFlux
Spring Boot Gradle Plugin
Spring Boot - Sending Email
Java Program to Construct a Random Graph by the Method of Random Edge Selection
Spring REST API + OAuth2 + Angular
Jackson – Marshall String to JsonNode
Lớp LinkedHashMap trong Java
Convert String to Byte Array and Reverse in Java
Giới thiệu Swagger – Công cụ document cho RESTfull APIs
Java Program to Implement Affine Cipher
Comparing Strings in Java
OAuth2 Remember Me with Refresh Token
Giới thiệu java.io.tmpdir
Spring Security OAuth Login with WebFlux
Spring Cloud Series – The Gateway Pattern
A Guide to the ViewResolver in Spring MVC
HttpClient 4 – Send Custom Cookie
The StackOverflowError in Java
Java Program to Implement LinkedTransferQueue API
Apache Commons Collections MapUtils
Introduction to Project Reactor Bus
Recommended Package Structure of a Spring Boot Project
Java Program to Implement Sorted Singly Linked List
Java Program to Implement Sorted Array
Java Program to Implement Sieve Of Eratosthenes