Validated Numerics: Numerics including mathematically strict error evaluation
Validated numerics (or reliable computation) is a numerical analysis with mathematically strict error evaluation.
In order to do so, a technology called interval arithmetic is used. Validated numerics is needed for the following reasons.
- It is difficult to avoid numerical errors in numerical computation, and computation without error evaluation may cause unfortunate results.
- It can be applied to computer-assisted proofs for mathematical problems.
One of the most known implementation of validated numerics is INTLAB (Interval Laboratory). INTLAB was used to create other numerical libraries, and it was also used to solve the Hundred-dollar, Hundred-digit Challenge problems.
References
Related pages
- Affine arithmetic
- Kantorovich theorem (A theorem frequently used in the context of validated numerics)
- Numerical digit
- Numerical integration
- Numerical linear algebra
- Numerical methods for ordinary differential equations
- Numerical methods for partial differential equations
- International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics
Other websites
- Validated Numerics for Pedestrians Archived 2021-05-09 at the Wayback Machine
- Reliable Computing, An open electronic journal devoted to validated numerics.
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