Precisionpreserving

Precisionpreserving refers to approaches in numerical computation and data representation that aim to maintain the original precision of numbers throughout processing. The core goal is to minimize or tightly bound rounding errors so that the final result remains faithful to exact arithmetic within predictable limits.

Techniques commonly described as precision-preserving include compensated arithmetic (such as Kahan summation and related error-free transformations), interval arithmetic that yields guaranteed bounds, and the use of higher- or arbitrary-precision arithmetic when needed. In programming, precision-preserving design also covers careful handling of data type conversions and serialization to avoid inadvertent loss of digits.

In numerical linear algebra, precision-preserving algorithms seek to avoid cancellation and growth of error during operations like summation, factorization, and solving equations. In scientific computing and engineering, such methods are valued for improved reliability and reproducibility, particularly in simulations sensitive to small perturbations.

Trade-offs exist: precision-preserving methods can incur additional computational overhead, memory usage, or implementation complexity. The choice to pursue precision preservation depends on problem sensitivity, available resources, and required guarantees. It is often considered alongside concepts such as numerical stability, backward error analysis, and exact or interval arithmetic.

See also: numerical analysis, floating-point arithmetic, numerical stability, compensated summation, interval arithmetic, arbitrary-precision arithmetic.