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 edithttps://docs.google.com/a/brandeis.edu/document/d/15FMUNqx3j1B2UR4ZXC--ajsfiTvGng4O6c5fQZSDA_A/edit?hl=en
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:
Topics to cover:
- 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
- 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...