Algorithms
A directory of methods that shape computational mathematics. Browse by subject or search for an algorithm, then follow its reference to learn more.
216 entries
Coding & information
Represent, compress, protect, and transmit information. This group also includes communication schemes and cryptographic constructions.
- Arithmetic coding
- Block Truncation Coding
- Code-division multiple access (CDMA)
- Convolutional codes
- Diffie–Hellman key exchange
- Elliptic-curve cryptography
- Embedded Zerotrees of Wavelet transforms
- Hamming codes
- Huffman coding
- Information theory
- JPEG 2000
- Lattice based cryptography
- Lempel–Ziv compression (LZ77)
- Low-density parity check codes
- Polar codes
- Reed-Solomon codes
- RSA
- Set partitioning in hierarchical trees
- Shor's Algorithm
- Time-division multiple access (TDMA)
- Turbo code
Arithmetic & polynomials
Compute with integers and polynomials, test primality, and solve algebraic problems.
Computer science & graphs
Search, sort, traverse networks, and organize discrete computations.
- A* search
- Bellman-Ford shortest paths
- Boyer–Moore string search
- Breadth-first search
- Chaitin graph coloring
- Dancing links
- Depth-first search
- Dijkstra’s shortest-path algorithm
- Dynamic programming
- Floyd–Warshall all pairs shortest path
- Girvan–Newman community detection
- Hashing
- Katz Centrality
- Knuth-Morris-Pratt string search
- Kruskal minimum-spanning-tree
- Locality sensitive hashing
- MapReduce
- Maximum subarray problem
- Needleman-Wunsch dynamic programming
- Planar graph embedding
- Prim’s minimum spanning tree
- Quicksort
- Radix sort
- Steinhaus-Johnson-Trotter permutation generation
- Tarjan’s strongly connected components
- Topological sorting
Numerical analysis & differential equations
Approximate integrals, evolve dynamical systems, and solve differential equations.
Matrices & linear algebra
Factorize matrices, solve linear systems, and exploit spectral or sparse structure.
- BiCGSTAB
- Cholesky decomposition
- Conjugate gradient
- Coppersmith-Winograd
- GMRES
- Golub–Reinsch singular value decomposition
- Hierarchical matrix
- Incomplete LU factorization
- Least-squares fitting
- LU decomposition
- Minimum degree sparse matrix reordering
- PageRank
- QR algorithm
- Sinkhorn matrix scaling
- Sparse matrix ordering
- Strassen matrix multiplication
Graphics & geometry
Represent curves and surfaces, construct meshes, and synthesize images.
- Alpha shapes
- B-splines
- Binary space partitioning
- Bowyer–Watson Delaunay triangulation
- Catmull–Clark Subdivision Surfaces
- de Boor's algorithm
- Delaunay refinement
- Floyd–Steinberg dithering
- Graham scan convex hull
- k-d tree nearest neighbor search
- Marching cubes
- Metropolis light transport
- Non-uniform rational B-spline
- Painter’s algorithm
- Path tracing
- Perlin noise
- Photon mapping
- Progressive meshes
- Ray tracing
- Semi-discrete optimal transport
- Sutherland–Hodgman polygon clipping
- Z buffer
Signals & images
Transform, reconstruct, filter, and compress signals and images.
- Anisotropic diffusion
- Basis pursuit
- Beurling Lasso and sparse super-resolution
- Block-matching and 3D filtering
- Canny edge detector
- Compressed sensing
- Discrete cosine transform (DCT)
- ESPRIT frequency estimation
- Fast Fourier transform
- Fast wavelet transform
- FastICA
- Gerchberg-Saxton phase retrieval
- Lifting scheme
- Matching pursuit
- Mathematical morphology
- Matrix pencil frequency estimation
- Mumford-Shah segmentation
- MUSIC frequency estimation
- Non-local means
- Orthogonal Wavelets
- PhaseLift phase retrieval
- Recursive Gaussian filtering
- SIFT
- Total variation denoising
Statistics & machine learning
Estimate models, classify observations, and learn useful representations from data.
- Aggregating algorithm
- Approximate Bayesian Computation
- Bagging (bootstrap aggregating)
- Baum-Welch HMM MLE
- Boosting
- Classification And Regression Tree
- Convolutional neural network
- DBSCAN clustering
- Dropout
- Empirical risk minimization
- Generative adversarial networks
- Hidden Markov model
- K-fold cross validation
- K-means / Lloyd’s algorithm
- k-nearest neighbor
- Kernel density estimation
- Kernel trick for SVM
- Lasso
- Latent Dirichlet Allocation
- Logistic regression
- Long short-term memory
- Maximum likelihood estimation
- Principal component analysis
- Probably approximately correct learning
- Random forests
- RANSAC parameter estimation
- Recurrent neural network
- Ridge regression
- Spectral clustering
- Support vector machine
Probability & sampling
Simulate random variables, sample distributions, and infer hidden states.
- Alias method
- Coupling from the past
- Expectation Maximization
- Gibbs sampling
- Hamiltonian Monte Carlo
- Importance sampling
- Junction tree for message passing
- Kalman filter
- Mersenne twister for random number generation
- Metropolis–Hastings
- Milstein method
- Nested-sampling
- Particle filter
- Reservoir sampling
- Sobol low-discrepancy sequences
- Sum-product message passing / belief propagation
- Tamed Euler method
- VEGAS Monte-Carlo
- Viterbi decoding / max-product message passing
Optimization
Minimize objectives, handle constraints, and solve continuous or discrete decision problems.
- Alternating direction method of multipliers
- Auction algorithm
- BFGS quasi-Newton method
- Branch and bound for combinatorial optimization
- Bregman iterative projections
- Burer–Monteiro low-rank factorization
- Conflict driven clause learning
- Cutting-plane mixed integer programming
- Douglas–Rachford splitting
- Dykstra’s projection algorithm
- Dynamic time warping
- Edmonds–Karp max-flow
- Espresso minimization algorithm
- Ford-Fulkerson maximum flow
- Forward–backward splitting
- Frank-Wolfe
- Gale-Shapley stable marriage
- Genetic algorithm
- Hungarian assignment algorithm
- Interior point method
- Levenberg-Marquardt
- Linear programming
- Majorize-Minimize
- Maxcut SDP relaxation
- Mirror descent
- Nelder–Mead derivative free method
- Nesterov’s accelerated gradient method
- Network simplex
- Newton’s Method
- Powell's method
- Proximal point algorithm
- Push-relabel maximum flow
- Reverse-mode automatic differentiation
- Simplex
- Simulated Annealing
- Steepest descent
- Stochastic gradient descent
- αBB global optimization
No methods match your search.
This collection includes both algorithms and mathematical models that can be solved in several ways. The subjects overlap: a method is listed in one group to make browsing easier. References provide definitions and historical context; the directory is not a ranking or an exhaustive history. Suggestions and corrections are welcome through the website repository.