Solution of tridiagonal linear equations

Do there have commands for cuda or open source code for solving equations of tridiagonal matrices with good acceleration effect

Not my area of expertise, but the publication below may provide a reasonable starting-point for your search. The abstract mentions a tridiagonal solver that is part of cuSPARSE.

Christoph Klein and Robert Strzodka, “Tridiagonal GPU Solver with Scaled Partial Pivoting at Maximum Bandwidth.” In 50th International Conference on Parallel Processing (ICPP ’21), August 9–12, 2021, Lemont, IL, USA. ACM, New York, NY, USA, 10 pages. https://doi.org/10.1145/3472456.3472484

Partial pivoting is the method of choice to ensure stability in matrix factorizations performed on CPUs. For sparse matrices, this has not been implemented on GPUs so far because of problems with datadependent execution flow. This work incorporates scaled partial pivoting into a tridiagonal GPU solver in such a fashion that despite the data-dependent decisions no SIMD divergence occurs. The cost of the computation is completely hidden behind the data movement which itself runs at maximum bandwidth. Therefore, the cost of the tridiagonal GPU solver is no more than the minimally required data movement. For large single precision systems with 225 unknowns, speedups of 5 are reported in comparison to the numerically stable tridiagonal solver (gtsv2) of cuSPARSE. The proposed tridiagonal solver is also evaluated as a preconditioner for Krylov solvers of large sparse linear equation systems. As expected it performs best for problems with strong anisotropies.

I just see there is a brand-new library by the same authors that may also be applicable to your use case:

Christoph Klein and Robert Strzodka, “tridigpu: A GPU library for block tridiagonal and banded linear equation systems.” ACM Transactions on Parallel Computing (January 2023). https://doi.org/10.1145/3580373

this may be of interest