Using level 3 BLAS in rotation-based algorithms. (English) Zbl 0912.65032

Lang, Bruno

SIAM J. Sci. Comput. 19, No. 2, 626-634 (1998).

From the author’s abstract: This paper presents a technique that allows using level 3 BLAS in a number of rotation-based algorithms. In particular, the update of an orthogonal transformation matrix which often involves the vast majority of operations can be done with a matrix-matrix product. The modifications do not affect the convergence properties of the algorithms nor do they significantly increase the overall number of operations. Thus, the computations can be speed up by more than 50% on machines with a distinct memory hierarchy.

Reviewer: Th.Sonar (Hamburg)

MSC:

65F15	Numerical computation of eigenvalues and eigenvectors of matrices
65Y20	Complexity and performance of numerical algorithms

Keywords:

BLAS 3; QR algorithm; performance modeling; rotation-based algorithms; convergence

Software:

BLAS; LAPACK