Computing the Bidiagonal SVD Through an Associated Tridiagonal Eigenproblem

On MR3-type Algorithms for the Tridiagonal Symmetric Eigenproblem and the Bidiagonal SVD

Lapack Working Note 166: Computing the Bidiagonal Svd Using Multiple Relatively Robust Representations

We describe the design and implementation of a new algorithm for computing the singular value decomposition of a real bidiagonal matrix. This algorithm uses ideas developed by Großer and Lang that extend Parlett’s and Dhillon’s MRRR algorithm for the tridiagonal symmetric eigenproblem. One key feature of our new implementation is, that k singular triplets can be computed using only O(nk) storag...

Computing the Bidiagonal SVD Using Multiple Relatively Robust Representations

We describe the design and implementation of a new algorithm for computing the singular value decomposition of a real bidiagonal matrix. This algorithm uses ideas developed by Großer and Lang that extend Parlett’s and Dhillon’s MRRR algorithm for the tridiagonal symmetric eigenproblem. One key feature of our new implementation is, that k singular triplets can be computed using only O(nk) storag...

A New O(n^2) Algorithm for the Symmetric Tridiagonal Eigenvalue/Eigenvector Problem

A New O(n) Algorithm for the Symmetric Tridiagonal Eigenvalue/Eigenvector Problem by Inderjit Singh Dhillon Doctor of Philosophy in Computer Science University of California, Berkeley Professor James W. Demmel, Chair Computing the eigenvalues and orthogonal eigenvectors of an n n symmetric tridiagonal matrix is an important task that arises while solving any symmetric eigenproblem. All practica...

An Accelerated Divide-and-Conquer Algorithm for the Bidiagonal SVD Problem

In this paper, aiming at solving the bidiagonal SVD problem, a classical divide-andconquer (DC) algorithm is modified, which needs to compute the SVD of broken arrow matrices by solving secular equations. The main cost of DC lies in the updating of singular vectors, which involves two matrix-matrix multiplications. We find that the singular vector matrices of a broken arrow matrix are Cauchy-li...