We present a new approach for sparse Cholesky factorization on a heterogeneous platform with a graphics processing unit (GPU). The sparse Cholesky factorization is one of the core algorithms of numerous computing applications. We tuned the supernode data structure and used a parallelization method for GPU tasks to increase GPU utilization. Results show that our approach substantially reduces computational time.

Fast and accurate estimation of missing relations, e.g., similarity, distance and kernel, among objects is now one of the most important techniques required by major data mining tasks, because the missing information of the relations is needed in many applications such as economics, psychology, and social network communities. Though some approaches have been proposed in the last several years, the practical balance between their required computation amount and obtained accuracy are insufficient for some class of the relation estimation. The objective of this paper is to formalize a problem to quickly and efficiently estimate missing relations among objects from the other known relations among the objects and to propose techniques called “PSD Estimation” and “Row Reduction” for the estimation problem. This technique uses a characteristic of the relations named “Positive Semi-Definiteness (PSD)” and a special assumption for known relations in a matrix. The superior performance of our approach in both efficiency and accuracy is demonstrated through an evaluation based on artificial and real-world data sets.

In this letter, a low complexity multi-cell joint channel estimation (MJCE) scheme is proposed. With proper arrangement of the multi-cell midamble matrix and channel impulse response (CIR) vector, the MJCE operation is formulated to solve a block-Toeplitz linear system. The block-Levinson algorithm is adopted to solve this problem instead of the Cholesky algorithm. Our results show that the proposed MJCE scheme can be a practical choice with significantly lower complexity, compared with the previous schemes with the Cholesky algorithm.

This paper focuses on fusion estimation algorithms weighted by matrices and scalars, and relationship between them is considered. We present new algorithms that address the computation of matrix weights arising from multidimensional estimation problems. The first algorithm is based on the Cholesky factorization of a cross-covariance block-matrix. This algorithm is equivalent to the standard composite fusion estimation algorithm however it is low-complexity. The second fusion algorithm is based on an approximation scheme which uses special steady-state approximation for local cross-covariances. Such approximation is useful for computing matrix weights in real-time. Subsequent analysis of the proposed fusion algorithms is presented, in which examples demonstrate the low-computational complexity of the new fusion estimation algorithms.