Machine epsilon is the smallest positive number that, when added to one, results in a value different from one in floating-point arithmetic. It reflects the limits of numerical precision in computing and is crucial for understanding error analysis and stability in numerical algorithms. This concept is essential in evaluating the accuracy of calculations and plays a significant role in algorithms such as Cholesky factorization, where precision impacts the stability and correctness of matrix computations.
congrats on reading the definition of machine epsilon. now let's actually learn it.