Let A 2 R mn be a matrix with known singular values and singular vectors, and let A 0 be the matrix obtained by appending a row to A. We present stable and fast algorithms for computing the singular values and the singular vectors of A 0 in O ? (m + n) min(m;n) log 2 2 oating point operations, where is the machine precision. Previous algorithms can be unstable and compute the singular values an...

In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...

We present in this paper a new method to determine the k largest singular values and their corresponding singular vectors for real rectangular matrices A ∈ Rn×m. Our approach is based on using a block version of the Power Method to compute an k-block SV D decomposition: Ak = UkΣkV T k , where Σk is a diagonal matrix with the k largest non-negative, monotonically decreasing diagonal σ1 ≥ σ2 · · ...