Algorithm classification
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- Vector operations
- Matrix-vector operations
- Matrix operations
- Matrix decompositions
- Triangular decompositions
- Gaussian elimination (finding the LU decomposition)
- Gaussian elimination without pivoting
- LU decomposition via Gaussian elimination
- Compact scheme for Gaussian elimination and its modifications
- Compact scheme for Gaussian elimination: Dense matrix
- Compact scheme for Gaussian elimination and its modifications: Tridiagonal matrix
- Gaussian elimination with pivoting
- Gaussian elimination with column pivoting
- Gaussian elimination with row pivoting
- Gaussian elimination with diagonal pivoting
- Gaussian elimination with complete pivoting
- Gaussian elimination without pivoting
- Cholesky method (finding the symmetric triangular decomposition)
- Cholesky decomposition (square root method): Basic pointwise real variant, dense symmetric positive definite matrix
- Available triangular decompositions for matrices of special form
- Gaussian elimination (finding the LU decomposition)
- Unitary-triangular decompositions
- Unitary Hessenberg decompositions
- Unitary-diagonal decompositions
- Triangular decompositions
- Solving systems of linear algebraic equations (SLAEs)
- Direct methods for solving SLAEs
- Linpack benchmark
- Methods for solving SLAEs of special forms
- Methods for solving triangular SLAEs
- Methods for solving tridiagonal SLAEs
- Methods based on the conventional LU decomposition
- Other methods
- Reduction method
- Two-sided Thomas algorithm
- Cyclic reduction
- Bordering method
- Methods for solving block triangular SLAEs
- Block forward substitution (real version)
- Block backward substitution (real version))
- Methods for solving block bidiagonal SLAEs
- Methods for solving block tridiagonal SLAEs
- Methods based on the conventional LU decomposition
- Other methods
- Solving SLAEs with coefficient matrices of special form whose inverses are known
- Iterative methods for solving SLAEs
- Direct methods for solving SLAEs
- Solving eigenvalue problems
- Computer performance tests
- Fourier transform
- Algebra of polynomials
- Numerical quadrature
- Graph algorithms
- Traversing a graph
- Single source shortest path (SSSP)
- Breadth-first search (BFS) (for unweighted graphs)
- Dijkstra's algorithm
- Bellman-Ford algorithm
- Δ-stepping algorithm
- All pairs shortest path (APSP)
- Transitive closure of a directed graph
- Longest shortest path
- Construction of the minimum spanning tree (MST)
- Search for isomorphic subgraphs
- Graph connectivity
- Shiloach-Vishkin algorithm for finding the connected components
- Disjoint set union
- Tarjan's strongly connected components algorithm
- DCSC algorithm for finding the strongly connected components
- Tarjan's biconnected components algorithm
- Tarjan-Vishkin biconnected components algorithm
- Tarjan's algorithm for finding the bridges of a graph
- Vertex connectivity of a graph
- Gabow's edge connectivity algorithm
- Finding maximal flow in a transportation network
- Finding minimal-cost flow in a transportation network
- Assignment problem
- Betweenness centrality algorithm
- Search algorithms
- Binary search: Finding the position of a target value within a sorted array, [math]O(log(n))[/math]
- Sorting algorithms
- Computational geometry
- Finding the diameter of a point set
- Finding the convex hull of a point set
- Delaunay triangulation
- Voronoi diagram
- Point-in-polygon problem
- Convex polygon intersection - complexity [math]O(n_1 + n_2)[/math]
- Star-shaped polygon intersection - complexity [math]O(n_1 * n_2)[/math]
- Computer graphics
- Cryptographic algorithms
- Neural networks
- Optimization algorithms
- Game theory algorithms
- Algorithms for quantum system simulation
- Algorithms for quantum computation simulation
- Algorithms for solving equations of mathematical physics
- Other algorithms