How much computational time does it take to find the inverse of a square matrix using Gauss Jordan method?  Part 1 of 2.

Problem Statement

How much computational time does it take to find the inverse of a square matrix using Gauss Jordan method?  Part 1 of 2.

Solution

To understand the solution, you should be familiar with the Gauss Jordan method of finding the inverse of a square matrix.  Peter Young of UCSC describes it briefly in this pdf file while if you like watching an example via a video, you can see PatrickJMT doing so.  You also need to read a previous blog where we calculated the computational time needed for the forward elimination steps on a square matrix in the Naïve Gauss elimination method.   We are now ready to estimate the computational time required for Gauss Jordan method of finding the inverse of a square matrix.

GJ Inverse Blog

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Euler’s Method Example for FE Exam

“The Fundamentals of Engineering (FE) exam is generally the first step in the process of becoming a professional licensed engineer (P.E.). It is designed for recent graduates and students who are close to finishing an undergraduate engineering degree from an EAC/ABET-accredited program” – FE Exam NCEES

For most engineering majors, numerical methods is a required portion of the math part of the examination. Here is an example of using Euler’s method to numerically solve an ordinary differential equation.

eulers_method_fe_exam.jpg

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Computational Time for Forward Elimination Steps of Naive Gaussian Elimination on a Square Matrix

Problem Statement

How much computational time does it take to conduct the forward elimination part of the Naïve Gauss Elimination method on a square matrix?

CTdecomposition

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Global truncation error in Euler’s method

Illustrate through an example that the global truncation error in Euler’s method is proportional to the step size.

euler_truncation_global_pic1
euler_truncation_global_pic2

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Resources for Numerical Methods

Are you taking or teaching a course in Numerical Methods in Spring 2018.   If so, then look at all these resources.

Open CourseWare:

YouTube:

MOOCS:

Blog:

Twitter: http://twitter.com/numericalguy 

Local truncation error is approximately proportional to square of step size in Euler’s method

Question: Show that the local truncation error in Euler’s method is proportional to the square of the step size.

euler_truncation_local_pic1euler_truncation_local_pic2

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I thought Gaussian quadrature requires that the integral must be transformed to the integral limit of [-1,1]?

Question asked on YouTube: I thought Gaussian quadrature requires that the integral must be transformed to the integral limit of [-1,1]?

The answer is given below.

gaussquadlimits

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