caa a22 4500 463203038 CHVBK 20180405153117.0 cr unu---uuuuu 170326e20070501xx s 000 0 eng 10.1007/s00200-007-0039-8 doi (NATIONALLICENCE)springer-10.1007/s00200-007-0039-8 Analysis of a sparse hypermatrix Cholesky with fixed-sized blocking [Elektronische Daten] [José Herrero, Juan Navarro] We present the way in which we have constructed an implementation of a sparse Cholesky factorization based on a hypermatrix data structure. This data structure is a storage scheme which produces a recursive 2D partitioning of a sparse matrix. It can be useful on some large sparse matrices. Subblocks are stored as dense matrices. Thus, efficient BLAS3 routines can be used. However, since we are dealing with sparse matrices some zeros may be stored in those dense blocks. The overhead introduced by the operations on zeros can become large and considerably degrade performance. We present the ways in which we deal with this overhead. Using matrices from different areas (Interior Point Methods of linear programming and Finite Element Methods), we evaluate our sequential in-core hypermatrix sparse Cholesky implementation. We compare its performance with several other codes and analyze the results. In spite of using a simple fixed-size partitioning of the matrix our code obtains competitive performance. Springer-Verlag, 2007 Sparse Cholesky nationallicence Hypermatrix structure nationallicence 2D partitioning nationallicence Windows in submatrices nationallicence Small Matrix Library nationallicence Herrero José Computer Architecture Department, Universitat Politècnica de Catalunya, Jordi Girona 1-3, Mòdul D6, 08034, Barcelona, Spain aut Navarro Juan Computer Architecture Department, Universitat Politècnica de Catalunya, Jordi Girona 1-3, Mòdul D6, 08034, Barcelona, Spain aut Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/3(2007-05-01), 279-295 0938-1279 18:3<279 2007 18 200 https://doi.org/10.1007/s00200-007-0039-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00200-007-0039-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Herrero José Computer Architecture Department, Universitat Politècnica de Catalunya, Jordi Girona 1-3, Mòdul D6, 08034, Barcelona, Spain aut NATIONALLICENCE 700 1- Navarro Juan Computer Architecture Department, Universitat Politècnica de Catalunya, Jordi Girona 1-3, Mòdul D6, 08034, Barcelona, Spain aut NATIONALLICENCE 773 0- Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/3(2007-05-01), 279-295 0938-1279 18:3<279 2007 18 200 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer