On a new iterative algorithm for solving linear equations

摘要: Abstract Let V and W be two real or complex spaces which, by means of the choice an inner product, we can identify with their duals. A : → a linear map. ′: its dual. There is very large number numerical algorithms (see [2] [3] for solving equation A·x=b . Some these algorithms, such as Gaussian elimination, produce entire k -dimensional affine solution space in , others, gradient methods [3], particular solution. It not always clear which they produce, indeed what criterion one ought to single out -parameter family. Here are interested solution, call canonical (1). We shall write R ( ) range r rank.