PPT-ACCELERATING SPARSE CHOLESKY FACTORIZATION ON GPUs

Dileep Mardham Introduction Sparse Direct Solvers is a fundamental tool in scientific computing Sparse factorization can be a challenge to accelerate using GPUs GPUsGraphics Processing Units can be quite good for accelerating sparse direct solvers. van de Geijn Department of Computer Science Institute for Computational Engineering and Sciences The University of Texas at Austin Austin TX 78712 rvdgcsutexasedu March 11 2011 1 De64257nition and Existence The Cholesky factorization is only de6 FORSGREN P E GILL AND W MURRAY SIAM J S CI OMPUT 1995 Society for Industrial and Applied Mathematics Vol 16 No 1 pp 139150 Abstract The e64256ectiveness of Newtons method for 64257nding an unconstrained minimizer of a strictly convex twice continuo 1 A complex matrix is hermitian if or ij ji is said to be hermitian positive de64257nite if Ax for all 0 Remark is hermitian positive de64257nite if and only if its eigenvalues are all positive If is hermitian positive de64257nite and LU is the LU utkedu Abstract We present a Cholesky factorization for multicore with GPU accelerators The challenges in developing scalable high performance al gorithms for these emerging systems stem from their heterogeneity mas sive parallelism and the huge gap The Cholesky factorization of allows us to e64259ciently solve the correction equations Bz This chapter explains the principles behind the factorization of sparse symmetric positive de64257nite matrices 1 The Cholesky Factorization We 64257rst show utkedu Abstract We present a Cholesky factorization for multicore with GPU accelerators The challenges in developing scalable high performance al gorithms for these emerging systems stem from their heterogeneity mas sive parallelism and the huge gap . Siddharth. . Choudhary. What is Bundle Adjustment ?. Refines a visual reconstruction to produce jointly optimal 3D structure and viewing parameters. ‘bundle’ . refers to the bundle of light rays leaving each 3D feature and converging on each camera center. . Direct. A = LU. Iterative. y. ’. = Ay. Non-. symmetric. Symmetric. positive. definite. More Robust. Less Storage. More Robust. More General. D. Column . Cholesky. Factorization. for. j = 1 : n. L(. &. Miriam . Leeser. Dana Brooks. mel@coe.neu.edu brooks@ece.neu.edu. 1. This . work . is supported by: . NSF . CenSSIS. - The Center for Subsurface Sensing and Imaging. 3. . Sparse Direct Method: . Combinatorics. Xiaoye . Sherry Li. Lawrence Berkeley National . Laboratory. , . USA. xsli@. lbl.gov. crd-legacy.lbl.gov. /~. xiaoye. /G2S3/. 4. th. Gene . Golub. SIAM Summer . Full storage:. . 2-dimensional array.. (nrows*ncols) memory.. 31. 0. 53. 0. 59. 0. 41. 26. 0. 31. 41. 59. 26. 53. 1. 3. 2. 3. 1. Sparse storage:. . Compressed storage by columns . (CSC).. Three 1-dimensional arrays.. Dense A:. Gaussian elimination with partial pivoting (LU). Same flavor as matrix * matrix, but more complicated. Sparse A:. Gaussian elimination – Cholesky, LU, etc.. Graph algorithms. Sparse A:. Contents. Problem Statement. Motivation. Types . of . Algorithms. Sparse . Matrices. Methods to solve Sparse Matrices. Problem Statement. Problem Statement. The . solution . of . the linear system is the values of the unknown vector . with. . BLIS. Kiran . varaganti. 19 September 2016. Contents. Introduction. libFLAME. Baseline Performance. Cholesky. QR. LU factorization. Analysis. Optimizations . Summary. Introduction. AMD provides high-performance computing libraries for various verticals:.