A Large Linear System Solver


GPU-accelerated algorithms for solving large sparse linear algebraic equations using C++ language, implementing Jacobi Method, Gauss—Seidel Method, Successive Over-Relaxation (SOR) Method, and Conjugate Gradient Method. Among these, we also implemented Jacobi Method and Conjugate Gradient using Nvidia CUDA API to accelerate these algorithms.

It is a collaborative, interdisciplinary project drawing on expertise from School of Software Engineering and College of Civil Engineering, Tongji University, Shanghai.

Getting Started

Environment Requirements

  • NVIDIA Graphics Card (Support at least versions after CUDA 10.0)
  • Microsoft Windows 10 (NVIDIA has ceased CUDA driver support for Apple MacOS X)
  • Microsoft Visual Studio (Special support for CUDA application)

Get the Project


* Only experiments of non-iterative methods are listed here.

Import the Project to IDE

  • Basic CPU versions (jacobi, gauss, SOR, conjugate gradient)

    • Use Visual Studio (2015/16/17/18) to create a Command Line Application project.
    • Copy the relevent .cpp, .h files to the project path xxx/src
    • You can also use compilers other than Visual Studio such as dev c++, llvm, ant etc.
  • CUDA GPU versions (jacobi_gpu, cg_gpu)

    • Use Visual Studio to create a blank CUDA project.
    • Copy the relevant .cu, .cuh, .cpp, .h, .lib, .exp files to the project path xxx/src
    • You can also use ncvv compilers (requires gcc and g++ on Linux, clang and clang++ on Mac OS X, and cl.exe on Windows)

Build the Project

In Visual Studio:

  • After configuring the compilation, click Build to build the project.

In Command Line:

  • If using g++ compiler, we strongly recommend you to turn on O3 compiler optimization using g++ -o3 command.

Running the Project

  • Install npm if missing npm environment
  • Enter project folder
    cd project
  • Run npm start
  • Open your browser and visit localhost://3000

Project Functionalities

  • Upload your matrix files (each includes a dense matrix and vector)
  • Solve the linear system using different algorithms


We use GitHub Wiki for organizing documentation. For the documentation available, see the homepage of our Wiki.

Code Structure

├── MatMul                         # Solve large matrix multiplication problem
│   ├── CUDA                       # Example provided by CUDA tutorial
│   ├── PyTorch&CuPy               # Cope with matrix multiplication using python libararies
│   └── cuBLAS                     # Solve large matrix multiplication using cuBLAS API
├── Iterative-Methods              # Implementation of iterative methods
│   ├── Basic                      # initialize solvers
│   ├── ConjugateGradient          # Conjugate Gradient method (both CPU and GPU)
│   ├── Jacobi                     # Jacobi method (both CPU and GPU)
│   ├── Gauss-Seidel               # Gauss Seidel method (both CPU and GPU)
│   ├── Sparse-Matrix-CG-Solver    # Solve sparse linear system using cuBLAS and cuSOLVER
│   └── Utils                      # Utils, helps to read matrix data from given file
├── Non-iterative-Methods          # Implementation of iterative methods
│   ├── Eigen                      # Gaussian Elimination, LU, SVD methods using Eigen
│   ├── Gaussian-elimination       # Gaussian Elimination method
│   ├── LU-Decomposition           # LU Decomposition method
│   └── svd-solver                 # SVD Decomposition method
├── project                        # A Node.js app for testing these algorithms
├── Report                         # Documentation for this project
├── README.md
└── images


This project is licensed under the Apache2.0 License - see the LICENSE.md file for details.

Zhaoyi Song
Zhaoyi Song
Master’s Student in Software Engineering