Two simple algorithms for the diagonalization of a set of sparse symmetric matrices of the form A+{Delta(k)}(k)(L)(=1) for large values of L are proposed and investigated. The numerical strategies economize computer resources by requiring the reconstruction of the Lanczos basis for a small number of times compared to L. Each member of the set {Delta(k)}(k)(L)(=1) is assumed to have a smaller number of nonzero elements compared to A. Both numerical procedures are derived from the Lanczos algorithm and use periodically a recursion to obtain the Lanczos vectors. Tests are conducted with both random symmetric matrices and with DVR Hamiltonians containing parametric potentials. The performance of the algorithms in terms of numerical accuracy, stability, and CPU time is studied as a function of two properties of the matrix set {Delta(k)}(k)(L)(=1).