Home Login  |   Contact  |   About Us       Tuesday, May 17, 2022   

j0185201- Back to Home
   Skip Navigation LinksHOME ›  AREAS OF EXPERTISE ›   Linear Equations  ›  ~ Gauss-Jordan



Skip Navigation Links.



"Linear Algebraic Equations"
Gauss-Jordan Elimination Method
Solution from the GAUSS-JORDAN elimination

X =

Matrix A: = { , , }, { , , }, { , , }

Vector b: = { , , }



[ Initial MatrixValues A: { 2, 1, 1 }, { 3, 1, 2 }, { 2, 1, 2 } ]
[ Initial VectorValues b: { 8, 11, 3 } ]

IMPLEMENTATION
Gauss-Jordan elimination

Solving sets of linear equations using Gauss-Jordan elimination produces both the solution of the equations and the inverse of the coefficient matrix. The Gauss-Jordan elimination process requires two steps. The first step, called the forward elimination, reduces a given system to either triangular or echelon form, or results in a degenerate equation indicating that the system has no solution. This is accomplished through the use of elementary operations. The second step, called the backward elimination, uses back-substitution to find the solution of the linear equations.

Iteration Algorithm Creation

In this method, the value of unknowns for triangulated equations are found, which can be done by using back-substitution. Starting with the last equation, which contains the single unknowns, a solution can be found immediately. This value may be substituted into the second last equation in order to calculate the next unknown. The process is repeated until all unknowns are found.

Testing Gauss-Jordan elimination Method

In order to test the method as defined above, a new TestGaussJordan() static method has been added and executed. Supporting code and methods are not shown.

A set of initial equations for the test has been defined for Matrix A and Vector b.

           static void TestGaussJordan();
              {
                 ListBox1.Items.Clear();
                 LinearSystem ls = new LinearSystem();
                 MatrixR A = new MatrixR(new double[3, 3] { { t1, t2, t3 }, { t4, t5, t6 }, { t7, t8, t9 } });
                 VectorR b = new VectorR(new double[3] { t10, t11, t12 });
                 VectorR x = ls.GaussJordan(A, b);
                 ListBox1.Items.Add("(" + x[0] + "," + x[1] + "," + x[2] + ")");
              }

An initial set of data points was defined for matrix A and vector b. The user can manipulate all values and try variations on the matrix and vector themselves.



Other Implementations...


Object-Oriented Implementation
Graphics and Animation
Sample Applications
Ore Extraction Optimization
Vectors and Matrices
Complex Numbers and Functions
Ordinary Differential Equations - Euler Method
Ordinary Differential Equations 2nd-Order Runge-Kutta
Ordinary Differential Equations 4th-Order Runge-Kutta
Higher Order Differential Equations
Nonlinear Systems
Numerical Integration
Numerical Differentiation
Function Evaluation


Consulting Services - Back to Home
Home

Home Math, Analysis,
  expertise..."

EIGENVALUE
SOLUTIONS...


> Rayleigh-Quotient Method

> Cubic Spline Method

 

Applied Mathematical Algorithms

Home

ComplexFunctions

Home

NonLinear
Home

Differentiation
Home

Integration
About Us


KMP Software Engineering is an independent multidisciplinary engineering consulting company specializing in mathematical algorithms.
Areas of
Expertise


SpecialFunctions
VectorsMatrices
OptimizationMethods
ComplexNumbers
Interpolation
CurveFitting
NonLinearSystems
LinearEquations
DistributionFunctions
NumericalDifferentiation
NumericalIntegration
DifferentialEquations
Smalltalk
FiniteBoundary
Eigenvalue
Graphics
Understanding
Mining


MiningMastery
MineralNews
MineralCommodities
MineralForum
Crystallography
Services


NumericalModeling
WebServices
MainframeServices
OutsourceServices

LINKED IN
KMP ARTICLES
Brand





Home

Login

Contact
Since 2006 All Rights Reserved  © KMP Software Engineering LINKS | PRIVACY POLICY | LEGAL NOTICE