This research work solves the problem of least squares that requires inner elipsoid algorithm to determine the descent direction; giving solution to linear programming problems by means of this methodof interior points. We solve the least squares problem using auxiliary function with logarithmic barrier and an approximation of the original matrix factorization by a matrix of rank one update to nally use the Sherman-Morrison-Woodburry formula and determining the inverse of the current matrix thus solving the least squares problem and obtaining a approximation to the descent direction.

This research work solves the problem of least squares that requires inner elipsoid algorithm to determine the descent direction; giving solution to linear programming problems by means of this methodof interior points. We solve the least squares problem using auxiliary function with logarithmic barrier and an approximation of the original matrix factorization by a matrix of rank one update to nally use the Sherman-Morrison-Woodburry formula and determining the inverse of the current matrix thus solving the least squares problem and obtaining a approximation to the descent direction.