In numerical analysis, the stability of an algorithm is the extent to which an approximation error in the calculation does not grow to be much bigger during the calculation. Given the great number of iterations that may be involved, this is a very real possibility. Since numerical analysis is concerned with finding approximate solutions to problems for which no analytical solution exists, it is an important consideration as to whether rounding or truncation errors in the algorithm are damped or amplified. Algorithms which can be shown not to magnify approximation errors are called numerically stable.