This paper presents linear algebra techniques used in the implementation of an interior point method for solving linear programs and convex quadratic programs with linear constraints. The new regularization techniques for Newton equation system applicable to both symmetric positive definite and symmetric indefinite systems are described. They transform the latter to quasidefinite systems known to be strongly factorizable to a form of Choleskylike factorization. Two different regularization techniques primal and dual suit very well the (infeasible) primal-dual interior point algorithm. This particular algorithm with an extension of multiple centrality correctors is implemented in our solver HOPDM. Computational results are given to illustrate the potential advantages of the approach applied to the solution of very large linear and convex quadratic programs