Two-way bidiagonalization scheme for downdating the singular-value decomposition Original Research Article

We present a method that transforms the problem of downdating the singular-value decomposition into a problem of diagonalizing a diagonal matrix bordered by one column. The first step in this diagonalization involves bidiagonalization of a diagonal matrix bordered by one column. For updating the singular-value decomposition, a two-way chasing scheme has been recently introduced, which reduces the total number of rotations by 50% compared to previously developed one-way chasing schemes. Here, a two-way chasing scheme is introduced for the bidiagonalization step in downdating the singular-value decomposition. We show how the matrix elements can be rearranged and how the nonzero elements can be chased away towards two corners of the matrix. The newly proposed scheme saves nearly 50% of the number of plane rotations required by one-way chasing schemes.