# Validatit numerics

numerical analysis wi mathematically strict error evaluation

Validatit numerics (or reliable computation) is a numerical analysis wi mathematically strict error evaluation[1][2]. I order tae dae sae, a technology callit interval arithmetic is usit[3][4][5]. Validatit numerics is needit for the followin reasons.

1. It is difficult tae avoid numerical errors i numerical computation, an computation without error evaluation may cause unfortunate results.
2. It can be appliit tae computer-assistit proofs for mathematical problems (such as pairtial differential equations)[6][7].

Ane o the most known implementation o validatit numerics is INTLAB[2][3][8][9] (Interval Laboratory). INTLAB wis usit tae create other numerical libraries, an it wis also usit tae solve the "Hundred-dollar, Hundred-digit Challenge problems"[10].

## References

1. Tucker, Warwick (2011). Validated Numerics: A Short Introduction to Rigorous Computations. Princeton University Press.
2. a b Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19, 287-449.
3. a b Moore, R. E., Kearfott, R. B., & Cloud, M. J. (2009). Introduction to Interval Analysis. Society for Industrial and Applied Mathematics.
4. Alefeld, G., & Mayer, G. (2000). Interval analysis: theory and applications. Journal of Computational and Applied Mathematics, 121(1-2), 421-464.
5. Mayer, G. (2017). Interval analysis: and automatic result verification. Walter de Gruyter GmbH & Co KG.
6. Meyer, K. R., & Schmidt, D. S. (Eds.). (2012). Computer aided proofs in analysis. Springer Science & Business Media.
7. M. Nakao, M. Plum, Y. Watanabe (2019) Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations (Springer Series in Computational Mathematics).
8. S.M. Rump: INTLAB - INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pages 77-104. Kluwer Academic Publishers, Dordrecht, 1999.
9. Hargreaves, G. I. (2002). Interval analysis in MATLAB. Numerical Algorithms, (2009.1).
10. Bornemann, F., Laurie, D., & Wagon, S. (2004). The SIAM 100-digit challenge: a study in high-accuracy numerical computing. Society for Industrial and Applied Mathematics.