A Fast Algorithm of Moore-Penrose Inverse for the Symmetric Loewner-Type Matrix

Abstract-Symmetric Loewner-type matrix has broad applications in natural sciences and engineering technologies. Many of the issues are summarized for the sake of symmetric Loewner (type) matrix and its correlation matrix algebraic problem. We present a new fast algorithm of Moore-Penrose inverse for an m×n symmetric Loewner-type matrix with full column rank by forming a special block matrix and studying its inverse in this paper. Its computation complexity is O(mn) + O(n
²
), but it is O(mn
²
) + O(n
³
) by using L
⁺
= (L
^T
L)
^-1
L
^T
. Experimental results also show that the former in terms of time and accuracy are better than the latter.