Improved parallel QR method for large least squares problems involving Kronecker products

[摘要] A new algorithm is presented for the efficient solution of large least squares problems in which the coefficient matrix of the linear system is a Kronecker product of two smaller dimension matrices. The solution algorithm is based on QR factorizations of the smaller dimension matrices. Near perfect load balancing is achieved by exploiting a 'commutativity' property of the Kronecker product, and communication requirements are minimized by employing a binary exchange algorithm for matrix transposition. The parallel algorithm is presented, and timing results are shown from test runs on an Intel i860 computer.

[发布日期] 1997-02-03

[关键词] Kronecker product;overdetermined least squares;QR factorization;matrix algorithms;parallel processing