Largescale triangular solver is an important computational kernel in scientific and engineering applications. However, execution of this kernel is not efficient on existing CPU and GPU platforms, due to limited cache capacity and the underlying problems of the architecture design. In the block solving of large-scale triangular linear equations, matrix multiplication is the main operation and its computational efficiency is crucial for improving the computational efficiency of solving triangular linear equations. Taking advantage of the high computation efficiency of the matrix multiplication coprocessor as the computing platform, and according its architectural features, we propose a block solving method and a performance analysis model of large-scale triangular linear equations on the matrix multiplication coprocessor. Experimental results show that a highly-efficient largescale triangular solver can be implemented on the matrix multiplication coprocessor with a computational efficiency up to 85.9%. Compared with the GPUs under the same process technology mode, the proposed triangular solver on the coprocessor can achieve 2.42× actual performance and 10.72× resource utilization.

large-scale, triangular linear equation, matrix multiplication, coprocessor