Algorithm classification

1. Vector operations
   1. Pairwise summation
   2. Dot product
2. Matrix-vector multiplication
   1. Dense matrix-vector multiplication
3. Matrix operations
   1. Dense matrix multiplication
4. Matrix decomposition
   1. Triangular decomposition
      1. Gaussian elimination
      2. Cholesky method
         1. Cholesky decomposition
   2. Unitary-triangular decomposition
   3. Decomposition into unitary and Hessenberg matrices
   4. Decomposition into unitary and diagonal matrices
5. Solution of linear equations systems
   1. Direct methods
      1. Matrices of a special form
         1. Triangular matrices
            1. Forward substitution
            2. Backward substitution
6. Computer benchmarks
7. Fourier transform
   1. Cooley–Tukey Fast Fourier Transform, radix-2 case
8. Algebra of polynomials
   1. Horner's method
9. Numerical integration methods
10. Graph algorithms
    1. Single Source Shortest Path (SSSP)
    2. All Pairs Shortest Path (APSP)
    3. Transitive closure of a directed graph
    4. Construction of the minimum spanning tree (MST)
    5. Search for isomorphic subgraphs
    6. Graph connectivity
    7. Finding maximal flow in a transportation network
    8. Assignment problem
11. Search algorithms
12. Sorting algorithms
13. Computational geometry
14. Computer graphics
15. Cryptographic algorithms
16. Neural networks
17. Optimization algorithms
18. Game theory algorithms
19. Algorithms of quantum system simulation
    1. Algorithms of quantum computation simulation
20. Algorithms for solving equations of mathematical physics
21. Other algorithms