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.

Efficient Implementation of QR Decomposition for Gigabit MIMO-OFDM Systems

Abstract: This paper presents a VLSI architecture of QR decomposition for 4×4 MIMO-OFDM systems. A real-value decomposed MIMO system model is handled and thus the channel matrix to be processed is extended to the size of 8×8. Instead of direct factorization, a QR decomposition scheme by cascading one complex-value and one real-value Givens rotation stages is proposed, which can save 44% hardware complexity. Besides, the requirement of skewed inputs in the conventional QR-decomposition systolic array is eliminated and 36% of delay elements are removed. The real-value Givens rotation stage is also constructed in a form of a stacked triangular systolic array to match with the throughput of the complex-value one. Hardware sharing is considered to enhance the utilization. The proposed design is implemented in 0.18-μm CMOS technology with 152K gates. From measurement, the maximum operating frequency is 100 MHz. It generates QR decomposition results every four clock cycles and accomplishes continuous projection every clock cycle to support MIMO detection up to 2.4 Gb/s. The measured power consumption is 318.6 mW and 219.6 mW for QR decomposition and projection, respectively, at the highest operating frequency. From the comparison, our proposed design achieves the highest throughput with high efficiency.

Parallel out-of-core computation and updating of the QR factorization

Abstract: This article discusses the high-performance parallel implementation of the computation and updating of QR factorizations of dense matrices, including problems large enough to require out-of-core computation, where the matrix is stored on disk. The algorithms presented here are scalable both in problem size and as the number of processors increases. Implementation using the Parallel Linear Algebra Package (PLAPACK) and the Parallel Out-of-Core Linear Algebra Package (POOCLAPACK) is discussed. The methods are shown to attain excellent performance, in some cases attaining roughly 80% of the “realizable” peak of the architectures on which the experiments were performed.

Parallel Tiled QR Factorization for Multicore Architectures

Abstract: As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these new processors. Fine grain parallelism becomes a major requirement and introduces the necessity of loose synchronization in the parallel execution of an operation. This paper presents an algorithm for the QR factorization where the operations can be represented as a sequence of small tasks that operate on square blocks of data. These tasks can be dynamically scheduled for execution based on the dependencies among them and on the availability of computational resources. This may result in an out of order execution of the tasks which will completely hide the presence of intrinsically sequential tasks in the factorization. Performance comparisons are presented with the LAPACK algorithm for QR factorization where parallelism can only be exploited at the level of the BLAS operations.

Comparison of orthogonal matching pursuit implementations

Abstract: We study the numerical and computational performance of three implementations of orthogonal matching pursuit: one using the QR matrix decomposition, one using the Cholesky matrix decomposition, and one using the matrix inversion lemma. We find that none of these implementations suffer from numerical error accumulation in the inner products or the solution. Furthermore, we empirically compare the computational times of each algorithm over the phase plane.

Computing Multivariate Fekete and Leja Points by Numerical Linear Algebra

Abstract: We discuss and compare two greedy algorithms that compute discrete versions of Fekete-like points for multivariate compact sets by basic tools of numerical linear algebra. The first gives the so-called approximate Fekete points by QR factorization with column pivoting of Vandermonde-like matrices. The second computes discrete Leja points by LU factorization with row pivoting. Moreover, we study the asymptotic distribution of such points when they are extracted from weakly admissible meshes.