In this paper, pseudo-inverse based estimation algorithms were proposed for the singular region. First, a new Recursive Least-Squares(RLS) algorithm based on matrix pseudo-inverse is proposed for generic linear model. The obtained recursive form is more simpler than that in the previous results. Secondly, the filtering in singular region is also considered by proposing a matrix pseudo-inverse based IIR filter with recursive form. It is shown via numerical studies that the proposed algorithms can overcome the divergence problem in the previous results, i.e., the numerical stability is improved with few computations of the matrix pseudo-inverse.