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.

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.