Fast Parallel Algorithms for QR and Triangular Factorization

Chun, Joohwan; Kailath, T.; Lev-Ari, H.

doi:10.1137/0908073

Cited by 143 publications

(44 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The matrix R is also known as the Cholesky factor of T H T. The Schur algorithm computes R and z = Q H x while exploiting the Block-Toeplitz structure of T. It starts by computing a displacement representation for T and x and then continues to gradually transform them into R and z by applying local unitary and hyperbolic transformations (Chun et al, 1987;Kailath and Chun, 1994).…”

Section: Displacement Representation and Schur Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

Incremental refinement of a multi-user-detection algorithm (II)

Vollmer

Götze

2003

Adv. Radio Sci.

View full text Add to dashboard Cite

Abstract. Multi-user detection is a technique proposed for mobile radio systems based on the CDMA principle, such as the upcoming UMTS. While offering an elegant solution to problems such as intra-cell interference, it demands very significant computational resources.In this paper, we present a high-level approach for reducing the required resources for performing multi-user detection in a 3GPP TDD multi-user system. This approach is based on a displacement representation of the parameters that describe the transmission system, and a generalized Schur algorithm that works on this representation. The Schur algorithm naturally leads to a highly parallel hardware implementation using CORDIC cells. It is shown that this hardware architecture can also be used to compute the initial displacement representation.It is very beneficial to introduce incremental refinement structures into the solution process, both at the algorithmic level and in the individual cells of the hardware architecture. We detail these approximations and present simulation results that confirm their effectiveness.

show abstract

Section: Displacement Representation and Schur Algorithmmentioning

confidence: 99%

“…m computes R and z = Q H x while exploiting the Block-. It starts by computing a displacement representation for T es to gradually transform them into R and z by applying local transformations (Chun et al, 1987;Kailath and Chun, 1994). presentation for T can be written down as…”

Section: Representation and Schur Algorithmmentioning

confidence: 99%

Incremental refinement of a multi-user-detection algorithm (II)

Vollmer

Götze

2003

Adv. Radio Sci.

View full text Add to dashboard Cite

show abstract

“…Here y, z andũ are inputs to the up/downdating procedures (ũ may differ slightly from the exact u becauseũ has been computed from (20)(21)). At this point we make no claims about the size of R b − R b and R t − R t .…”

Section: From (16)mentioning

confidence: 99%

“…We do not consider this here, except to note that our algorithm can easily be modified to compute the Cholesky factorisation of A T A + αI, where α is a positive regularisation parameter. Only small changes in equations (20)(21)(22)(23) are required.…”

Section: Ill-conditioned Problemsmentioning

confidence: 99%

“…Unfortunately, Sweet's algorithm depends on the condition of a certain submatrices of A, so is unstable [8,56]. Other O(n 2 ) algorithms for computing the matrices Q and R or R −1 in (1) were given by Bojanczyk, Brent and de Hoog [8], Chun, Kailath and Lev-Ari [21], Cybenko [23], Luk and Qiao [56,64], and Nagy [60]. To our knowledge none of them has been shown to be stable.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stability analysis of a general toeplitz systems solver

1995

View full text Add to dashboard Cite

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R T R is close to A T A. Thus, when the algorithm is used to solve the semi-normal equations R T Rx = A T b, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem min Ax − b 2 .

show abstract

A Novel Data‐Driven Bilinear Subspace Identification Approach

Yang

2007

Can J Chem Eng

View full text Add to dashboard Cite

Les méthodes d'identifi cation du sous-espace pour les systèmes bi-linéaires permettent d'effectuer des calculs par ordinateur avec des matrices de données qui explosent. L'extrême lourdeur des calculs par ordinateur constitue le problème majeur qui empêche d'appliquer en pratique l'identifi cation du sous-espace bi-linéaire. Dans cet article, nous proposons une nouvelle approche d'identifi cation du modèle de prédiction bilinéaire à partir de données d'entrée-sortie qui présente une effi cacité de calcul améliorée. Basée sur la théorie des structures de déplacement, la factorisation QR est remplacée par une factorisation de Cholesky rapide, qui permet de traiter l'obstacle de la très grande dimensionnalité et réduit donc les coûts de calcul. Ces améliorations rendent l'approche du sous-espace bi-linéaire plus effi cace en termes de calcul par ordinateur avec une bonne capacité de prédiction. Enfi n, la méthode de contrôle proposée est illustrée par une simulation d'un système de réacteur continu parfaitement agité (CSTR).

show abstract

Fast Parallel Algorithms for QR and Triangular Factorization

Cited by 143 publications

References 21 publications

Incremental refinement of a multi-user-detection algorithm (II)

Incremental refinement of a multi-user-detection algorithm (II)

Stability analysis of a general toeplitz systems solver

A Novel Data‐Driven Bilinear Subspace Identification Approach

Contact Info

Product

Resources

About