Numerical Literacy in R—First Draft

[oleks]

Give a concise summary of Chapter 1 of Accuracy and Stability of Numerical Algorithms,
Nicholas J. Higham, 2002, with a
particular emphasis on R and IEEE-754 double-precision binary floating-point,
the default floating-point type in R. In particular, Section 1.18, "Designing Stable
Algorithms" gives some advice on how to keep things stable. The initial draft
should only illustrate the instability that results from doing things "by
hand", and show how e.g. using built-in functions, and vectorizing your code can
help maintain numerical stability. The first draft is not intended to define any
additional constructs, beyond those already available in R.

Contrary to what seems to be the tradition (e.g. 2), focus on giving demotivating examples rather than saying things like "numerically it can be disastrous" — convince the reader by showcasing a "disaster".

Another good source seems to be Numerical Methods in Finance and Economics: A MATLAB®-Based Introduction, Paolo Brandimarte, 2006, also wrt. option pricing using Monte Carlo methods.

• The IEEE-754 double-precision binary floating-point format
  • Binary Approximation
  • Scientific Notation
  • Basic Operations
• Computing sums
• Computing means and sample variance

[kfl]

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