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.
Papers published on a yearly basis
Papers
More filters
TL;DR: The collocation points are placed on concentric spheres and thus the resulting global matrix possesses a block circulant structure, which is exploited to develop an efficient matrix decomposition algorithm for the solution of the resulting system.
Abstract: In this study, we propose an efficient algorithm for the evaluation of the particular solutions of three-dimensional inhomogeneous elliptic partial differential equations using radial basis functions. The collocation points are placed on concentric spheres and thus the resulting global matrix possesses a block circulant structure. This structure is exploited to develop an efficient matrix decomposition algorithm for the solution of the resulting system. Further savings in the matrix decomposition algorithm are obtained by the use of fast Fourier transforms. The proposed algorithm is used, in conjunction with the method of fundamental solutions for the solution of three-dimensional inhomogeneous elliptic boundary value problems.
24 citations
TL;DR: A fast new algorithm for reducing an N × N quasiseparable matrix to upper Hessenberg form via a sequence of N − 2 unitary transformations, yielding lower cost and a simplification of implementation.
24 citations
TL;DR: In this paper, a thermodynamically consistent finite deformation continuum model is developed to simulate the thermomechanical response of shape memory polymers (SMPs) under simple shear deformation.
24 citations
01 Jun 2010
TL;DR: An efficient implementation of the Modified SParse Approximate Inverse (MSPAI) preconditioner is presented, introducing two new optimization techniques that reduce the runtime spent on the most demanding numerical parts as the code switches to sparse QR decomposition methods wherever profitable.
Abstract: We present an efficient implementation of the Modified SParse Approximate Inverse (MSPAI) preconditioner. MSPAI generalizes the class of preconditioners based on Frobenius norm minimizations, the class of modified preconditioners such as MILU, as well as interface probing techniques in domain decomposition: it adds probing constraints to the basic SPAI formulation, and one can thus optimize the preconditioner relative to certain subspaces. We demonstrate MSPAI's qualities for iterative regularization problems arising from image deblurring. Such applications demand for a fast and parallel preconditioner realization. We present such an implementation introducing two new optimization techniques: First, we avoid redundant calculations using a dictionary. Second, our implementation reduces the runtime spent on the most demanding numerical parts as the code switches to sparse QR decomposition methods wherever profitable. The optimized code runs in parallel with a dynamic load balancing.
24 citations
TL;DR: In this article, the authors considered the problem of efficiently computing the eigenvalues of limited-memory quasi-Newton matrices that exhibit a compact formulation, and proposed a compact formula for quasiNewton matrix generated by any member of the Broyden convex class of updates.
Abstract: In this paper, we consider the problem of efficiently computing the eigenvalues of limited-memory quasi-Newton matrices that exhibit a compact formulation. In addition, we produce a compact formula for quasi-Newton matrices generated by any member of the Broyden convex class of updates. Our proposed method makes use of efficient updates to the QR factorization that substantially reduce the cost of computing the eigenvalues after the quasi-Newton matrix is updated. Numerical experiments suggest that the proposed method is able to compute eigenvalues to high accuracy. Applications for this work include modified quasi-Newton methods and trust-region methods for large-scale optimization, the efficient computation of condition numbers and singular values, and sensitivity analysis.
24 citations