SSP2021@NiigataUniv
Introduction to Verified Numerical Computation (Verified Computing)
Feb.15 2021

Kazuaki TANAKA

Links

• Cloud Education System (CES)
  developed by X.Liu.
• kv Library
  A C++ Library for verified numerical computations.
• VCP Library
  A C++ Library for verified numerical computations for partial differential equaitions.
  The VCP Library has useful marix classes and is applicable to rigorously computing solutions of a system of equations using kv Library.
• INTLAB (for your information)
  A Matlab/Octave toolbox for Reliable Computing.

References

• Introduction to verified computation, 2019 (K.Sekine)
  Today, often refer to this.
• Interval Analysis, R.E.Moore, etc
  Probably the first book about interval arithmetic.
• IEEE 754 standard
  The standard of floating point numbers.
• Publication, S.Oishi
• Publication, S.M.Rump
  The following are surveys for verified computing for linear systems written by S.M.Rump:
  • Journal of Computational and Applied Mathematics 242 (2013) 157–184.
  • Journal of Computational and Applied Mathematics 242 (2013) 185–212.
• Publication, A.Neumaier

Lecture Slides

• Introduction
• Floating point numbers
• Interval Arithmetics
• System of linear equations
• Application to PDEs (Tanaka's interest, for your information)

Programs

• All (zip file)
• optimization_1.cc