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Topic: Gauss Jordan elimination

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  Gauss-Jordan Elimination
Gauss-Jordan Elimination is a variant of Gaussian Elimination.
In Gauss-Jordan Elimination, the goal is to transform the coefficient matrix into a diagonal matrix, and the zeros are introduced into the matrix one column at a time.
However, we will show later that Gauss-Jordan elimination involves slightly more work than does Gaussian elimination, and thus it is not the method of choice for solving systems of linear equations on a computer.
ceee.rice.edu /Books/CS/chapter2/linear44.html   (439 words)

 Gauss elimination
Gaussian elimination solves this linear system of equations by converting the original equations, using elementary row operations, to a simpler form that allows a simple substitution process.
An alternative procedure, Gauss-Jordan elimination, uses elementary row operations to both zero the elements below the diagonal and above.
However, Gauss-Jordan elimination is less efficient in usage of computer resources than Gaussian elimination.
home.att.net /~srschmitt/script_gauss_elimination5.html   (307 words)

  Gauss Jordan Elimination
During the process of Gauss-Jordan elimination all matrices are row equivalent to the original and each other.
The difficult part of Gauss-Jordan elimination is the bit in the middle—deciding which columns to manipulate and how to convert them in to leading 1s.
This is Gauss Jordan Elimination by Simon Willison, posted on 1st October 2002.
www.simon.incutio.com /archive/2002/10/01/gaussJordanElimination   (1940 words)

  Gauss-Jordan Elimination   (Site not responding. Last check: 2007-11-02)
The initial matrix is reduced to diagonal form by applying a sequence of elementary elimination matrices to annihilate both the subdiagonal and superdiagonal entries in successive columns.
The same sequence of elementary elimination matrices is also applied to an auxiliary matrix that is initially the identity matrix.
When Gauss-Jordan elimination is complete, the remaining diagonal matrix on the left is scaled to produce an identity matrix, at which point the matrix on the right will be the inverse of the original matrix.
www.cse.uiuc.edu /eot/modules/linear_equations/gauss_jordan   (317 words)

 PlanetMath: row reduction
A variant of Gaussian elimination is Gauss-Jordan elimination.
In this variation we reduce to echelon form, and then if the system proves to be consistent, continue to apply the elementary row operations until the augmented matrix is in reduced echelon form.
In essence, Gauss-Jordan elimination performs the back substitution; the values of the unknowns can be read off directly from the terminal augmented matrix.
planetmath.org /encyclopedia/GaussianElimination.html   (519 words)

 Calculating Matrix Determinant Using Gauss-Jordan Elimination   (Site not responding. Last check: 2007-11-02)
However, the full-fledged version of the elimination is not needed.
This elimination comes into play due to the fact that if the elements in lower triangle of the matrix are all zeroes, the determinant is simply the product of the diagonals.
So, the elimination works to shape the matrix into one of these forms.
www.geocities.com /codeteacher/misc/misc20011214-0000.html   (254 words)

 Bicycle   (Site not responding. Last check: 2007-11-02)
The process of Gauss elimination involves a series of matrix operations that reduce an augmented matrix into simpler forms from which the solution set of a system of equations can be more easily determined.
Gauss elimination leaves a matrix in lower triangular form, with ones (1's) on the diagonal.
In order to perform Gauss elimination most effectively, ERO's should be performed on a column-by-column basis, starting at the first column and ending at the second-to-last column.
links.math.rpi.edu:16080 /devmodules/bicycle/html/gauss.html   (331 words)

 Results for 'Jordan'
Jordan elimination on a matrix of 0's and 1's...
the speedup is acceptable for the Gauss Elimination and Gauss-
Jordan but for Jacobi with dominant rows if data is not...
odysseus.ieee.org /ieeesearch/query.html?qt=Jordan   (262 words)

 TI-82 Gauss Jordan Elimination
This program inputs the dimensions M and N of a matrix, the exactness R of the calculation, and the matrix [E], and then calculates the reduced row echelon form ("RREF") of [E].
The algorithm used is the standard Gauss Jordan Elimination Algorithm (without pivoting), as described e.g.
Remarks on rounding errors: Unfortunately, the Gauss Jordan Elimination Algorithm is not stable with respect to rounding errors; that means that accumulated rounding errors do not only change the numbers of the output a little, but they can in fact dramatically change the outcome: Instead of e.g.
www.math.sunysb.edu /calculus/rowred-ti82.html   (1315 words)

 Gauss Programs - Matrix Inverse Calculator, Micro Economy Model
This program uses the complicated Gauss Jordan elimination method to find the...
The idea of this model is to understand the behavior of the variables related...
The interface also is so good and it has many features other than a single diary.
www.softchecker.com /files/gauss.html   (224 words)

 Study Guide
The process of using row operations to solve linear systems is called Gaussian elimination.
Gaussian elimination can be used to determine the number of solutions for systems with three or more equations.
Q: Use Gaussian elimination to find the complete solution to the system of equations, or show that none exists.
wps.prenhall.com /esm_blitzer_algtrig_2/0,7303,911522-,00.html   (1395 words)

 Gauss-Jordan Elimination
Use the improved Gauss-Jordan elimination subroutine with row interchanges to solve
The print statements are for pedagogical purposes and are not needed.
The Gauss-Jordan elimination method is the "heuristic" scheme found in most linear algebra textbooks.
math.fullerton.edu /mathews/n2003/GaussianJordanMod.html   (470 words)

 Gauss-Jordan Elimination   (Site not responding. Last check: 2007-11-02)
To invert a matrix, Gauss-Jordan elimination is a good method.
In addition to solving sets of matrix equations with one or more righthand sides b, Gauss-Jordan elimination finds the matrix inverse A-1.
However, Gauss-Jordan elimination is the way most students have learned to solve matrix equations by hand, it is quite a stable method if implemented with full pivoting, and it is always useful to have alternative ways of doing something.
eyrie.shef.ac.uk /lec4/sld006.html   (132 words)

 Systems of Linear Equations: Gaussian Elimination
However, though the method of solution is addition/elimination, just trying to do addition would get very messy, so there is a systematized method for solving the three-or-more-variables systems.
Note: While Gaussian elimination reduces the messiness of solving, you will still need plenty of scratch paper for doing the steps.
And Gaussian elimination is the method we'll use to convert systems to this upper triangular form, using the row operations we learned when we did the addition method.
www.purplemath.com /modules/systlin6.htm   (897 words)

 Gauss Jordan Elimination
During the process of Gauss-Jordan elimination all matrices are row equivalent to the original and each other.
The difficult part of Gauss-Jordan elimination is the bit in the middle—deciding which columns to manipulate and how to convert them in to leading 1s.
Hi, Dear sir, D you have the code to solve gauss elimination using Mat Lab, if you do so, please, would you send that to me? Thank you.
simonwillison.net /2002/Oct/1/gaussJordanElimination   (1940 words)

 Solving Systems of Equations
This activity is designed to help you understand the process of solving systems of equations using Gauss-Jordan Elimination on the augmented coefficient matrix.
The final form of a matrix during the Gauss-Jordan elimination process.
It is as much like the Identity matrix as it is possible to transform the original matrix using elementary row operations.
www.saintmarys.edu /~psmith/338act2.html   (1955 words)

 Gauss Jordan elimination   (Site not responding. Last check: 2007-11-02)
Johnathan Spingarn and Xuelei Wang have several resources for Gauss Jordan elimination with examples in Maple.
However, Gauss -Jordan elimination is only used by the numericaly illiterate, as it is always extra work over LU, but has no advantage.
It is one of those methods that is forced upon students in linear algebra courses, but is of no use to anyone outside of passing a linear algebra final exam.
coweb.math.gatech.edu:8888 /model/50   (110 words)

 Gauss-Jordan Elimination
Gaussian elimination gives us tools to solve large linear systems numerically.
It is done by manipulating the given matrix using the elementary row operations to put the matrix into row echelon form.
For the sake of not sounding redundant, back substitution is doing steps 3-7 going back up the diagonal.
www.aspire.cs.uah.edu /textbook/gauss.html   (781 words)

 Pivoting Methods
If, then row p cannot be used to eliminate the elements in column p below the main diagonal.
Because the computer uses fixed-precision arithmetic, it is possible that a small error will be introduced each time that an arithmetic operation is performed.
The scale factors are interchanged with their corresponding row in the elimination steps.
math.fullerton.edu /mathews/n2003/PivotingMod.html   (586 words)

 Do you know how to solve Linear Equations using the Gauss - Jordan elimination method ? - FORMATCV.com   (Site not responding. Last check: 2007-11-02)
Do you know how to solve Linear Equations using the Gauss - Jordan elimination method ?
You can use 'Linear Equations Solver' using the Gauss - Jordan elimination method (303 kb).
Click on Mode button and the green straight line will be changed in stair line.
www.formatcv.com /182.html   (230 words)

 C and C++ - Gauss-Jordan Elimination on Matrices | DreamInCode.net
Hi guys, I'm new to c++, i'm writing code to do Gauss-Jordan elimination on a matrix.
It is doing it almost correctly, except that every other entry in my inverse is coming up as zero! There must be a problem with my loops, but the numbers that ARE there are correct, so it must be something minor.
void matrix::triangulate(matrix anda, vector andb, vector andx){ //this is the centrepiece of my class, it does gauss elimination, and prepares the matrix for backsubstitution by getting ones on the diagonals.
www.dreamincode.net /forums/showtopic21597.htm   (1467 words)

 Gauss Jordan Elimination Algorithm   (Site not responding. Last check: 2007-11-02)
Systems of linear equations can be solved using Gauss-Jordan Elimination (also known as RREF: Row Reduced Echelon Form).
The program rref demonstrate how you can use Gauss Jordan Elimination to solve linear system of equations using a programming language.
It was written in C, but you can rewrite it easily in any language you know well.
math.utoledo.edu /~dbastos/gauss_jordan.html   (279 words)

 Gauss - Jordan Elimination Program
This program is useful for illustrating the Gauss - Jordan elimination method of solving a system of linear equations.
It allows the user to focus on the method and not get bogged down by the arithmetic.
If this is OK then the result is next inserted in the second row (equation).
mathonweb.com /gauss.htm   (219 words)

 Best free gauss jordan method downloads. Mathematical program for university students. Mathematical program for ...
Gauss jordan method software: Mathematical program for university students, Mathematical program for university students, Geodata of the Federal Republic of Germany and more.
Find its inverse matrix by using the Gauss-Jordan elimination method.
The program gives a complete, step-by-step solution of the following problem: Given a 2x2 linear system (two equations, two variables) or 2x3, or 3x2, or 3x3, or 3x4, or 4x3, or 4x4 linear system.
www.freedownloadmanager.org /downloads/gauss_jordan_method_software   (149 words)

 Matrix Inverse Calculator 1.0 - Uses a complicated method to find the inverse of any square matrix
This program uses the complicated Gauss-Jordan elimination method to find the inverse of any square matrix.
You simply choose your matrix's dimensions, and then enter the elements of the matrix you want inverted in the left frame.
Calculate, Calculator, Download, Elimination, Gauss, Inverse, Jordan, Math, Mathematics, Matrices
www.downloadthat.com /windows/Educational/Mathematics/Matrix-Inverse-Calculator.html   (254 words)

 Mathematics Archives - Topics in Mathematics - Linear Algebra
Course materials, lecture notes, linear functions, linear algebra review, orthonormal vectors and QR factorization, least-squares methods, regularized least-squares and minimum norm methods, autonomous linear dynamical systems, eigenvectors and diagonalization, Jordan canonical form, aircraft dynamics, symmetric matrices, quadratic forms, matrix norm, and SVD, quantum mechanics, controllability and state transfer
Rank, Determinant, Trace, Signature, Powers, Exponential, Characteristic polynomial of A, Eigenvalues and eigenvectors, Jordan form.
Gauss Jordan row reduction and the simplex method
archives.math.utk.edu /topics/linearAlgebra.html   (662 words)

 Solve Systems of 3 Linear Equations By Matrices: Using Gauss-Jordan Elimination
Solve Systems of 3 Linear Equations By Matrices: Using Gauss-Jordan Elimination
Solve Systems of 3 Linear Equations by Matrices: Gauss-Jordan Elimination
Click in Equation 1, 2, 3 text boxes.
www.cyberedinc.com /HowTo/Slv3GJE.htm   (37 words)

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