Updating the singular value decomposition

LetA be anm×n matrix with known singular value decomposition. The computation of the singular value decomposition of a matrixA is considered, whereA is obtained by appending a row or a column toA whenm?n or by deleting a row or a column fromA whenm>n. An algorithm is also presented for solving the updated least squares problemA y?b?, obtained from the least squares problemAx?b by appending an equation, deleting an equation, appending an unknown, or deleting an unknown.