Suppose $A$ is an $m \times n$ matrix in the form

$$A=\begin{pmatrix} — a_1 —\\ — a_2 —\\ \vdots \\ — a_m — \end{pmatrix}$$

where $a_i \in R^n$ is the $i$-th row of $A$. I know that it is possible to determine the nullspace of $A$ by QR decomposition. This decomposition can be obtained with the Gram-Schmidt process, which takes one *column* of $A$ into account at each step of the procedure.

I am looking for direct/fast iterative algorithms with low time complexity which can be utilized to compute the exact/approximate values for a set of vectors that spans the the nullspace (kernel) of $A$ by taking one *row* of $A$ into account at each step. Are there any?