This article reports an unexpected and rather erratic behavior of the LAPACK software implementation of the QR factorization with Businger-Golub column pivoting. It is shown that, due to finiteâ€¦ (More)

This article proposes an efficient algorithm for reducing matrices to generalized Hessenberg form by unitary similarity, and recommends using it as a preprocessor in a variety of applications. Toâ€¦ (More)

This paper introduces a new algorithm for solving large-scale continuous-time algebraic Riccati equations (CARE). The advantage of the new algorithm is in its immediate and efficient low-rankâ€¦ (More)

Since numerical libraries are used in engineering design in a variety of industrial applications, it is important that their numerical reliability is the top priority of both the developers ofâ€¦ (More)

Any symmetric matrix can be reduced to antitriangular form in finitely many steps by orthogonal similarity transformations. This form reveals the inertia of the matrix and has found applications in,â€¦ (More)

This paper proposes a combination of a hybrid CPUâ€“GPU and a pure GPU software implementation of a direct algorithm for solving shifted linear systems (Aâˆ’ ÏƒI)X = B with large number of complex shiftsâ€¦ (More)

The QZ algorithm for computing eigenvalues and eigenvectors of a matrix pencil A âˆ’ Î»B requires that the matrices first be reduced to Hessenberg-triangular (HT) form. The current method of choice forâ€¦ (More)

This paper introduces a new algorithm for solving large-scale continuoustime algebraic Riccati equations (CARE). The advantage of the new algorithm is in its immediate and efficient low-rankâ€¦ (More)