Matrix stretching for sparse least squares problems

Strengths and Limitations of Stretching for Least-squares Problems with Some Dense Rows

“…original normal matrix; this is consistent with the upper bound on the condition number of the stretched system presented by Adlers and Björck [2] (see also Reference [44]).…”

Prestructuring sparse matrices with dense rows and columns via null space methods

“…Matrix stretching: This approach was originally designed to transform dense rows/columns/blocks in M for solving least‐squares problems, where M T M must be formed . This can be applied to problems of the form with dense B 2 by introducing auxiliary “linking” variables and splitting the rows of B 2 via the linking variables.…”

“…To compare the performance of the new method with matrix stretching, the matrix row stretching technique discussed in of Section 4.4 was implemented. Computations were performed for the mixed Navier–Stokes systems in Section 5.2.2 and the dual‐mixed Stokes problem on the irregular mesh in Section 5.2.3.…”

A Computational Study of Using Black-box QR Solvers for Large-scale Sparse-dense Linear Least Squares Problems

“…The serial HSL QR package MA49 [29] was developed in the 1990s [4]; more recently, there is SuiteSparseQR of Davis [15] 1 and qr_mumps of Buttari [12]. 2 These are general-purpose multifrontal sparse QR packages, and the latter two are designed to exploit parallelism. It is not our intention to try and compare these codes or to assess their efficiency for solving general sparse LS problems: our interest is in using an existing sparse QR package without modification to solve mixed sparse-dense LS problems.…”

“…The idea was proposed by Grcar [26] and was subsequently used in a number of different contexts for solving linear systems [3,6,18,19]. Stretching has also been applied to LS problems [1,2]. Stretching treats the dense rows one by one.…”