Improved parallel solution of a triangular linear system

The Parallel Solution of Triangular Systems of Linear Equations

We present a parallel algorithm for solving triangular systems of linear equations on distributed-memory multiprocessor machines. The parallelism is achieved by partitioning the rows of the coefficient matrix in segments of a fixed size and distributing these sets in a wrap-around fashion among the processors, connected in a ring. The granularity of the algorithm is controlled by varying the se...

Structure-adaptive parallel solution of sparse triangular linear systems

Solving sparse triangular systems of linear equations is a performance bottleneck in many methods for solving more general sparse systems. Both for direct methods and for many iterative preconditioners, it is used to solve the system or improve an approximate solution, often across many iterations. Solving triangular systems is notoriously resistant to parallelism, however, and existing paralle...

On Parallel Solution of Sparse Triangular Linear Systems in CUDA

The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Significant performance enhancements have been achieved for many sparse matrix computational kernels such as sparse matrix-vector products and sparse matrix-matrix products. Solving linear systems with sparse triangular struc...

Highly Parallel Sparse Triangular Solution

Parallel complexity of linear system solution

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