The total least squares (TLS) techniques, also called orthogonal regression and errors-in-variables modeling, see [15, 16], have been developed independently in several areas. For a given linear (orthogonally invariant) approximation problem AX ≈ B, where A ∈ Rm×n, B ∈ Rm×d, X ∈ Rn×d, the TLS formulation aims at a solution of a modified problem (A + E)X = B + G such that min ‖[G,E]‖F . The alge...

We give a systolic algorithm and array for bidiagonalization of an n x n matrix in O(nlog, n) time, using O(n2) cells. Bandedness of the input matrix may be effectively exploited. If the matrix is banded, with p nonzero subdiagonals and q nonzero superdiagonais, then 4n In(p + q) + O(n) clocks and 2n(p + q ) + O((p + q)’ + n) cells are needed. This is faster than the best previously reported re...

Methods for updating the LU factors of simplex basis matrices are reviewed. An alternative derivation of the Fletcher and Matthews method is given. This leads to generalizations of their method which avoids problems with both the Bartels and Golub method and the Fletcher and Matthews method. The improvements are to both numerical stability and data access locality. The resulting updating algori...

For the accurate approximation of the minimal singular triple (singular value and left and right singular vector), we may use two separate search spaces, one for the left, and one for the right singular vector. In Lanczos bidiagonalization, for example, such search spaces are constructed. In [3], the author proposes a Jacobi–Davidson type method for the singular value problem, where solutions t...

With the increasing use of high-resolution multimedia streams and large image and video archives in many of today’s research and application areas, there is a growing need for multimedia-oriented highperformance computing. As a consequence, a need for algorithms, methodologies, and tools that can serve as support in the (automatic) parallelization of multimedia applications is rapidly emerging....

Computation of singular value decomposition (SVD) has been a topic of concern by many numerical linear algebra researchers. Fast SVD has been a very effective tool in computer vision in a number of aspects, such as: face recognition, eye tracking etc. At the present state of the art fast and fixed-point power efficient SVD algorithm needs to be developed for real-time embedded computing. The wo...