Topic
QR decomposition
About: QR decomposition is a research topic. Over the lifetime, 3504 publications have been published within this topic receiving 100599 citations. The topic is also known as: QR factorization.
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01 Jul 2014
TL;DR: This paper presents a new stable algorithm for the parallel QR-decomposition of ''tall and skinny'' matrices based on the fast but unstable CholeskyQR algorithm and provides promising results of the MPI-based implementation on a BlueGene/P and a Power6 system.
Abstract: In this paper we present a new stable algorithm for the parallel QR-decomposition of ''tall and skinny'' matrices. The algorithm has been developed for the dense symmetric eigensolver ELPA, where the QR-decomposition of tall and skinny matrices represents an important substep. Our new approach is based on the fast but unstable CholeskyQR algorithm (Stathopoulos and Wu, 2002) [1]. We show the stability of our new algorithm and provide promising results of our MPI-based implementation on a BlueGene/P and a Power6 system.
16 citations
06 Dec 2020
TL;DR: A real-time capable Forward Kinematics (FK) algorithm for Cable-Driven Parallel Robots (CDPRs) considering the pulley kinematics is proposed and results address the convergence capabilities of the proposed algorithm.
Abstract: A real-time capable Forward Kinematics (FK) algorithm for Cable-Driven Parallel Robots (CDPRs) considering the pulley kinematics is proposed. The algorithm applies iteratively QR decomposition to solve a linearized version of the least squares problem representing the FK. Differential kinematics delivers an analytical expression for the Jacobian matrix of CDPRs considering the pulley kinematics. This Jacobian matrix is used to construct the linearization of the FK problem. Experimental and numerical results address the convergence capabilities of the proposed algorithm.
16 citations
TL;DR: In this article, several methods of solving input estimation problems, which take the form of structured block matrix problems, are studied in structural mechanics and a criterion for choosing the level of regularization based on the data used to construct L-curves is suggested.
16 citations
23 Jul 2013
TL;DR: A shape morphing procedure is introduced that dynamically matches the layout to the computation throughout the algorithm, and it is shown that Gaussian Elimination with partial pivoting can be performed in a communication efficient and cache-oblivious way.
Abstract: High performance for numerical linear algebra often comes at the expense of stability. Computing the LU decomposition of a matrix via Gaussian Elimination can be organized so that the computation involves regular and efficient data access. However, maintaining numerical stability via partial pivoting involves row interchanges that lead to inefficient data access patterns. To optimize communication efficiency throughout the memory hierarchy we confront two seemingly contradictory requirements: partial pivoting is efficient with column-major layout, whereas a block-recursive layout is optimal for the rest of the computation. We resolve this by introducing a shape morphing procedure that dynamically matches the layout to the computation throughout the algorithm, and show that Gaussian Elimination with partial pivoting can be performed in a communication efficient and cache-oblivious way. Our technique extends to QR decomposition, where computing Householder vectors prefers a different data layout than the rest of the computation.
16 citations
23 Feb 1988
TL;DR: A new projection-based algorithm for estimating the angles of arrival of plane waves incident onto arrays of sensors based on a single QR decomposition of the signal covariance matrix, which is much faster than eigen-based methods which require many QR decompositions.
Abstract: We propose a new projection-based algorithm for estimating the angles of arrival of plane waves incident onto arrays of sensors. The method is based on a single QR decomposition of the signal covariance matrix; hence, it is much faster than eigen-based methods which require many QR decompositions. It is shown that optimum performance is attained only if the columns of the covariance matrix are permuted in a prescribed manner before the QR decomposition proceeds. An adjunct to the angle of arrival estimation process is a new eigenvalue-free technique for estimating the number of incident signals. There is no performance penalty associated with either of these new methods. The real-time performance of this technique is enhanced through the use of systolic arrays. A novel systolic array structure is proposed for extracting both the Q and R matrices generated by the QR decomposition.
16 citations