The proper orthogonal decomposition is a numerical method that enables a reduction in the complexity of computer intensive simulations such as computational fluid dynamics and structural analysis (like crash simulations). Typically in fluid dynamics...
In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a scaling, followed by another rotation. It generalizes the eigendecomposition of a square normal matrix with an...
Model order reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations. As such it is closely related to the concept of metamodeling, with applications in all areas of mathematical...
Sparse identification of nonlinear dynamics (SINDy) is a data-driven algorithm for obtaining dynamical systems from data. Given a series of snapshots of a dynamical system and its corresponding time derivatives, SINDy performs a sparsity-promoting...
In data science, dynamic mode decomposition (DMD) is a dimensionality reduction algorithm developed by Peter J. Schmid and Joern Sesterhenn in 2008. Given a time series of data, DMD computes a set of modes, each of which is associated with a fixed...
In mathematics, a semiorthogonal decomposition is a way to divide a triangulated category into simpler pieces. One way to produce a semiorthogonal decomposition is from an exceptional collection, a special sequence of objects in a triangulated...
Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing. The data are linearly transformed onto a new coordinate system such that the...
In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem states that a stochastic process can be represented as an infinite linear combination...
The orthogonal Procrustes problem is a matrix approximation problem in linear algebra. In its classical form, one is given two matrices A {\displaystyle A} and B ...