List of Numerical Analysis Topics - General

General

• Iterative method
• Rate of convergence — the speed at which a convergent sequence approaches its limit
• Series acceleration — methods to accelerate the speed of convergence of a series
  • Aitken's delta-squared process — most useful for linearly converging sequences
  • Minimum polynomial extrapolation — for vector sequences
  • Richardson extrapolation
  • Shanks transformation — similar to Aitken's delta-squared process, but applied to the partial sums
  • Van Wijngaarden transformation — for accelerating the convergence of an alternating series
• Abramowitz and Stegun — book containing formulas and tables of many special functions
  • Digital Library of Mathematical Functions — successor of book by Abramowitz and Stegun
• Curse of dimensionality
• Local convergence and global convergence — whether you need a good initial guess to get convergence
• Superconvergence
• Discretization
• Difference quotient
• Complexity:
  • Computational complexity of mathematical operations
  • Smoothed analysis — measuring the expected performance of algorithms under slight random perturbations of worst-case inputs
• Symbolic-numeric computation — combination of symbolic and numeric methods
• Cultural aspects:
  • International Workshops on Lattice QCD and Numerical Analysis
  • Hundred-dollar, Hundred-digit Challenge problems — list of ten problems proposed by Nick Trefethen in 2002
• General classes of methods:
  • Collocation method — discretizes a continuous equation by requiring it only to hold at certain points
  • Level set method
    • Level set (data structures) — data structures for representing level sets
  • Sinc numerical methods — methods based on the sinc function, sinc(x) = sin(x) / x
  • ABS methods