March 2011 – Numerical Methods Guy

Computational Time for Back Substitution

This is a blog that will show you how we can find the approximate time it takes to conduct back substitution, while solving simultaneous linear equations using Gaussian elimination method. The blog assumes a AMD-K7 2.0GHz chip that uses 4 clock cycles for addition, subtraction and multiplication, and 16 clock cycles for division. Note that we are making reasonable approximations in this blog. Our main motto is to find how the computational time is related to the number of equations.

The pdf file of the solution is also available.

This post is brought to you by

Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.mathforcollege.com,
the textbook on Numerical Methods with Applications available from the lulu storefront,
the textbook on Introduction to Programming Concepts Using MATLAB, and
the YouTube video lectures available at http://nm.mathforcollege.com/videos

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Taylor Series Exercise – Method 3

Taylor series is an important concept for learning numerical methods – not only for understanding how trigonometric and transcendental functions are calculated by a computer, but also for error analysis in numerical methods. I asked the question below in the first test in the course, and half of the students did not get to the final answer. In a previous blog, I showed you the method that most instructors would use. See how some students approached (another approach) the problem.

Taylor Series Exercise Method 3