Iterative methods

This Presentation can be used by the Students of Engineering who Deals with the Subject ENGINEERING MATHEMATICS IV and use it for Refrence (Anyways you Guys will Copy Paste or Download it) ;)

1. PREPARED BY KETAN NAYAK (140413117005) HARSH PARMAR (140413117006) SAWAN PARMAR (140413117007) Chandan pathAK (140413117008) ASHISH PATIL(140413117009) INSTRUMENTATION and Control DEPT NUMERICAL TECHINIQUES & STATISTICAL METHODS

2. LINEAR SYSTEM SOLUTION USING ITERATIVE METHODS Sr. No TITLE 1. INTRODUCTION 2. ITERATION METHODS 3. JACOBI’S METHOD 4. GAUSS SEIDEL METHOD 5. APPLICATION OF ITERATION METHODS

3. INTRODUCTION In various applications of Engineering the Linear Algebraic Equations occurs quite often. The Solution of such system of the Equations can be obtained by Direct Methods or Iterative Method. Here we are Going to Talk about the VARIOUS ITERATIVE METHODS used in Engineering.

4. ITERATIVE METHODS Whenever the Algebraic Equations contains large no of equations at that time DIRECT METHOD becomes lengthy and Time Consuming Headache. In this Case the Iteration methods plays a Vital Role by being the Substitute of the Method. In Iterative methods we start from an Initial Approximation to actual Solution & obtain the better Approximation after Repeating the ITERATION. This method gives Desired Accuracy.

5. Jacobi Method The Jacobi method is a method of solving a matrix equation on a matrix that has no zeros along its main diagonal (Bronstein and Semendyayev 1997, p. 892). Each diagonal element is solved for, and an approximate value plugged in. The process is then iterated until it converges.

6. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The Jacobi method is easily derived by examining each of the n equations in the linear system of equations Ax =b in isolation. If, in the ith equation sum_(j=1)^na_(ij) x_j = b_i ,

7. GAUSS SIEDEL METHOD It is a iterative method used to solve a linear system of equation. It uses the latest value to find the value of next variable.

8. APPLICATIONS Analysis of the Circuit containing the Invariant Elements. Determination of Output of Chemical Plants. Study of the Civil Engineering Structures. Problems of Layered Media in Siesmology etc.