Numerical analysis is a branch of applied mathematics that studies certain specialized techniques for solving mathematical problems; in particular, it is the study of algorithms that use numerical approximation for mathematical analysis problems. In general, it employs mathematical axioms, theorems, and proofs, and often uses empirical results to further analyze or examine new methods. Characteristics of numerical analysis methods include accuracy (the numerical approximation should be as accurate as possible); robustness (the algorithm should be able to solve many problems and should relate to the user when the results are inaccurate); and speed (the faster the computation, the better the method).