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.

Performance of random sampling for computing low-rank approximations of a dense matrix on GPUs

Abstract: A low-rank approximation of a dense matrix plays an important role in many applications. To compute such an approximation, a common approach uses the QR factorization with column pivoting (QRCP). Though the reliability and efficiency of QRCP have been demonstrated, this deterministic approach requires costly communication at each step of the factorization. Since such communication is becoming increasingly expensive on modern computers, an alternative approach based on random sampling, which can be implemented using communication-optimal kernels, is becoming attractive. To study its potential, in this paper, we compare the performance of random sampling with that of QRCP on an NVIDIA Kepler GPU. Our performance results demonstrate that random sampling can be up to 12.8x faster than the deterministic approach for computing the approximation of the same accuracy. We also present the parallel scaling of the random sampling over multiple GPUs on a single compute node, showing a speedup of 3.8x over three Kepler GPUs. These results demonstrate the potential of the random sampling as an excellent computational tool for many applications, and its potential is likely to grow on the emerging computers with the increasing communication costs.

Efficient Calculation of Minimum Distance Between Capsules and Its Use in Robotics

Abstract: The problem of minimum distance calculation between line-segments/capsules, in 3D space, is an important subject in many engineering applications, spanning CAD design, computer graphics, simulation, and robotics. In the latter, the human–robot minimum distance is the main input for collision avoidance/detection algorithms to measure collision imminence. Capsules can be used to represent humans and objects, including robots, in a given dynamic environment. In this scenario, it is important to calculate the minimum distance between capsules efficiently, especially for scenes (situations) that include a high number of capsules. This paper investigates the utilization of QR factorization for performing efficient minimum distance calculation between capsules. The problem is reformulated as a bounded variable optimization in which an affine transformation, deduced from QR factorization, is applied on the region of feasible solutions. A geometrical approach is proposed to calculate the solution, which is achieved by computing the point closest to the origin from the transferred region of feasible solutions. This paper is concluded with numerical tests, showing that the proposed method compares favorably with the most efficient method reported in the literature.

Review of Matrix Decomposition Techniques for Signal Processing Applications

Abstract: Decomposition of matrix is a vital part of many scientific and engineering applications. It is a technique that breaks down a square numeric matrix into two different square matrices and is a basis for efficiently solving a system of equations, which in turn is the basis for inverting a matrix. An inverting matrix is a part of many important algorithms. Matrix factorizations have wide applications in numerical linear algebra, in solving linear systems, computing inertia, and rank estimation is an important consideration. This paper presents review of all the matrix decomposition techniques used in signal processing applications on the basis of their computational complexity, advantages and disadvantages. Various Decomposition techniques such as LU Decomposition, QR decomposition , Cholesky decomposition are discussed here.

Systolic-array based regularized QR-decomposition for IEEE 802.11n compliant soft-MMSE detection

Abstract: This paper considers the implementation of a soft-output MMSE detector for packet-based MIMO-OFDM transmission. The paper focuses on channel-matrix preprocessing realized with a QR decomposition which needs to be carried out under tight latency constraints. We discuss how the preprocessing algorithm should be selected to meet the specific requirements of the soft-output MMSE detector. Additionally we develop a pipelined systolic-array architecture that is particularly well suited to be combined with low-latency pipelined FFTs. We have implemented the QR decomposition method proposed for an IEEE 802.11n transceiver with 4 spatial streams. In a 0.13 µm 1P8M CMOS technology the corresponding circuit is capable to process 110 complex-valued 4×4-dimensional channel matrices for soft-output MMSE detection per second and gate equivalent and achieves a sustained throughput of 20 million decompositions per second, which is sufficient to meet the stringent latency requirements of IEEE 802.11n.