Solving linear algebraic equations without error

Introduces a new recursive algorithm for solving highly ill-conditioned linear algebraic equations without any cutoff error. It has the following properties: (1) all arithmetic operations are just related to integer additions, abstractions, multiplications, and divisions that can be precisely completed without any remainder; (2) the results of every recursion could be verified automatically by the algorithm itself, and (3) the total arithmetic operations are comparable with those of other direct methods. This algorithm is specially suitable for solving the highly ill-conditioned equations; it can also be used in digital signal processing and other related areas.< >