Gauss & Gauss-Seidel Numerical Methods
Universidad Autónoma de Querétaro
Facultad de Ingeniería
“Iterative Methods”
“Gauss and Gauss-Seidel”
Profesor | | Nieves Fonseca Ricardo | Mentado Camacho Félix
Navarro Escamilla Erandy
Péloquin Blancas María José
Rubio Miranda Ana Luisa
Abstract
Many real life problems give us several simultaneous linear equations to solve. And we have to find a common solution for each of them. There are several techniques to use.
Instead of using methods that provide a solution to a set of linear equations after a finite number of steps, we can use a series of algorithms with fewer steps, but its accuracy depends on the number of times it is applied (also known as iterative methods). For large systems they may be a lot faster than direct methods.
We will expand on two important methods to find numerical solutions to linear systems of equations. There will be an introduction to each method, besides detailed explanations on each of them.
Normally each process is long, so they are ideal for programming.
Keywords
Iterative, algorithm, linear equation, convergence.
Objective
Understand the concepts of iterative methods, and convergence, besides the difference and usefulness between direct and iterative methods. To give a clear and understandable idea of Gauss
and Gauss-Seidel methods to solve systems of linear equations, and show how to apply them.
Investigation
Iterative method
An iterative method is one that computes approximations in a progressive way of the solution of a mathematical problem. The same improvement process is repeated on the approximate solution until a solution closer to the real value is obtained. Differently than a direct method, which entails finishing the process to get an answer, on an iterative one the process can be stopped when an iteration is finished to get an approximation to the solution.
Advantages and disadvantages
The bad thing about iterative methods is that they
Facultad de Ingeniería
“Iterative Methods”
“Gauss and Gauss-Seidel”
Profesor | | Nieves Fonseca Ricardo | Mentado Camacho Félix
Navarro Escamilla Erandy
Péloquin Blancas María José
Rubio Miranda Ana Luisa
Abstract
Many real life problems give us several simultaneous linear equations to solve. And we have to find a common solution for each of them. There are several techniques to use.
Instead of using methods that provide a solution to a set of linear equations after a finite number of steps, we can use a series of algorithms with fewer steps, but its accuracy depends on the number of times it is applied (also known as iterative methods). For large systems they may be a lot faster than direct methods.
We will expand on two important methods to find numerical solutions to linear systems of equations. There will be an introduction to each method, besides detailed explanations on each of them.
Normally each process is long, so they are ideal for programming.
Keywords
Iterative, algorithm, linear equation, convergence.
Objective
Understand the concepts of iterative methods, and convergence, besides the difference and usefulness between direct and iterative methods. To give a clear and understandable idea of Gauss
and Gauss-Seidel methods to solve systems of linear equations, and show how to apply them.
Investigation
Iterative method
An iterative method is one that computes approximations in a progressive way of the solution of a mathematical problem. The same improvement process is repeated on the approximate solution until a solution closer to the real value is obtained. Differently than a direct method, which entails finishing the process to get an answer, on an iterative one the process can be stopped when an iteration is finished to get an approximation to the solution.
Advantages and disadvantages
The bad thing about iterative methods is that they
Bibliography: George W. Collins, II Fundamental Numerical Methods and Data Analysis Chapter 2 Online edition from http://ads.harvard.edu/books/1990fnmd.book/ Métodos Numéricos: Gauss Jordan y Gauss Seidel http://www.scribd.com/doc/21428959/Gauss-Jordan-Gauss-Seidel Métodos iterativos para resolver sistemas lineales http://www.mty.itesm.mx/etie/deptos/m/ma95-843/lecturas/l843-13.pdf