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lecture 07

Wednesday 2/9/2011

Video of the lecture is available at http://dennett.cs-i.brandeis.edu/cs177/L7
The diary of the lecture and the .m files are attached at the end of this page.

Also, here is a link to a latex file in google docs that Brandeisians can edit
The pdf generated by this is attached at the end of this file.

Reading: we are covering material from Chapters 6 and 7 of the Matlab book by Amos Gilat.

Learning Objectives for today:
students will
  • be able to write an octave/matlab function computing a mathematical function defined by its Taylor series using both a for loop and with vector operations alone (e.g. hw3)
  • understand the time and space tradeoffs for these two ways of writing the function
  • be able to explain the different sources of error in Scientific Computing
  • be able to plot the relative approximation error for a function they have written (assuming they have an authoritative function to compare it to).
  • write simple functions involving for, while, and if statements to compute numberic values

Topics to cover:
  • Taylor series approximations of special functions
    • writing exp, sin directly
    • writing them without loops!
    • modified exponential for any x
  • Error in Numerical Computation
    • machine error (e.g. Pentium FDIV bug)
    • floating point numbers (IEEE754) and roundoff error
    • approximation error and eps(x)
    • modeling error
    • measurement error
  • More examples of matlab/octave functions:
    • Statistics procedures written from scratch (mean, stdev)
    • Matrix multiplication written from scratch
  • Useful Matlab functions:
    • ind=find(array) returns a list of indices where the array is non-zero
    • use this to select subsets of vectors/matrices according to their properties...
Timothy Hickey,
Feb 10, 2011, 5:49 AM
Timothy Hickey,
Feb 10, 2011, 5:38 AM
Timothy Hickey,
Feb 10, 2011, 5:39 AM