Exploring different encodings of matrix algebra in order to implement algorithms for solving systems of linear equations from “An introduction to the conjugate gradient method without the agonizing pain”.

• MatrixAlgebra1: 2-by-2 matrices and vectors using tuples
• MatrixAlgebra1.CG1: Solution techniques from article
• MatrixAlgebra2: 2^n-by-2^n matrices using a recursive representation

• PowerSeries: Code from “Power series, power serious”

• Simple to use (implements Num class).
• If there is to be numerical work in the course ireal would probably be suitable if Double does not give good enough precision.
• Some nested operations might become exponential (as documented in https://github.com/sydow/ireal/raw/master/doc/ireal.pdf). It seems good understanding of the library is necessary to avoid them.
• Contains example implementations of algorithms using the package. applications/FAD.hs has a short implementation of AD that might be interesting.

• http://conal.net/papers/beautiful-differentiation/
• http://hackage.haskell.org/package/ad

• Real numbers: http://hackage.haskell.org/package/numbers
• Intervals: http://hackage.haskell.org/package/intervals
• real numbers+intervals: https://hackage.haskell.org/package/ireal