This paper describes a recursive method for the LU factorization of sparse matrices. The recursive formulation of common linear algebra codes has been proven very successful in dense matrix computations. An extension of the recursive technique for sparse matrices is presented. Performance results given here show that the recursive approach may perform comparable to leading software packages for...

In this work we present new kernels for the generation and application of block-Jacobi preconditioners that accelerate the iterative solution of sparse linear systems on graphics processing units (GPUs). Our approach departs from the conventional LU factorization and decomposes the diagonal blocks of the matrix using the Gauss-Huard method. When enhanced with column pivoting, this method is as ...

For a vector function, coded without branches or loops, code for the Jacobian is generated by interpreting Griewank and Reese’s Vertex Elimination as Gaussian elimination, and implementing this as compact LU factorization. Tests on several platforms show such code is typically 4 to 20 times faster than that produced by tools such as Adifor, Tamc or Tapenade, on average significantly faster than...

This paper describes our progress in developing software for performing parallel LU factorization of a large dense matrix on a GPU cluster. Three approaches, with increasing software complexity, are considered: (i) a naive “thunking” approach that links the existing parallel ScaLAPACK software library with cuBLAS through a software emulation layer; (ii) a more intrusive magmaBLAS implementation...

Gaussian elimination based sparse LU factorization with partial pivoting is important to many scientiic applications, but it is still an open problem to develop a high performance sparse LU code on distributed memory machines. The main diiculty is that partial pivoting operations make structures of L and U factors unpredictable beforehand. This paper presents an approach called S for paralleliz...