The paper considers methods of mathematical computations acceleration taking into account architectural features of central and graphic processors. A complex approach to optimization of biconjugate gradient method computations is existed, aimed at increasing performance when solving problems with large dimensions, which is particularly important for artificial intelligence, where efficient linear algebra operations form the computational core of many algorithms. The main attention is paid to the development of a modified algorithm of the biconjugate gradient method, including the optimization of matrix-vector multiplication and vector updating. Modern tools based on BLAS standards (including OpenBLAS, MKL and cuBLAS) and parallel programming technologies SYCL and OpenCL have been applied to implement the algorithms. We also analyzed the influence of architectural characteristics of processors on the speed of computations. The paper presents a modified version of the algorithm of the biconjugate gradient method with the combination of matrix updating and transposition stages, and also improves the convergence criterion, which increases stability and reduces the number of iterations. The algorithms are tested on both CPU and GPU with detailed performance and accuracy analyses. As a result, a significant reduction in computation time compared to standard implementations is achieved. Experimental results show that the use of optimized algorithms and adaptive allocation of computational resources can significantly reduce the execution time of linear algebra problems and improve the efficiency of computational processes. Conclusions about the expediency of adapting algorithms for specific architectural features of processors to obtain maximum performance in the conditions of distributed computing systems are formulated. The given approach demonstrates high efficiency in solving problems with intensive computational loads, which is confirmed by the obtained experimental data.