The Schläfli graph is an interesting and well-studied graph in the field of graph theory, particularly in relation to polyhedra and higher-dimensional polytopes. It is defined as the graph whose vertices correspond to the regular polyhedra (in 3D) and regular polytopes (in higher dimensions), and where edges connect pairs of polyhedra that share a common face.

A table of simple cubic graphs provides a list of cubic graphs, which are graphs where every vertex has a degree of exactly 3 (i.e., each vertex is connected to exactly three edges). Simple cubic graphs have no loops or multiple edges between the same pair of vertices. These graphs are also known as 3-regular graphs. A common way to organize and present simple cubic graphs is by their number of vertices (usually denoted as \( n \)).

A triangle graph, often referred to in the context of graph theory, can denote different concepts based on context, but generally it refers to a type of graph structure that contains a specific relationship resembling triangles. 1. **Triangle in Graph Theory**: In a general mathematical graph, a triangle is a complete subgraph consisting of three vertices, where each vertex is connected to the other two. This means there are three edges that form a triangle shape.

Dune is an open-source build system used primarily in the OCaml programming language ecosystem. It streamlines the process of building projects written in OCaml and ReasonML, providing developers with a more efficient way to manage dependencies, compile code, and create project structures. Dune automates many tasks associated with building projects, such as dependency resolution, managing multiple source files, and generating necessary build configurations.

ILNumerics is a numerical computing library designed for .NET environments, particularly useful for data science and scientific computing applications. It provides a range of functionalities for handling complex mathematical operations efficiently, including support for multi-dimensional arrays, linear algebra, numerical optimization, and data visualization. Key features of ILNumerics include: 1. **Performance**: ILNumerics is optimized for high-performance computations, leveraging the capabilities of .NET and native code, often using optimized libraries for linear algebra and numerical computations.

A Data Analytics Library refers to a collection of tools, functions, and methods designed to facilitate the analysis of data. These libraries provide programmers and data scientists with the necessary functions to manipulate, analyze, and visualize data efficiently. Common features of data analytics libraries include: 1. **Data Manipulation**: Functions for cleaning, transforming, and aggregating data, such as filtering, grouping, and merging datasets.

The Gauss-Seidel method is an iterative technique used to solve a system of linear equations of the form \(Ax = b\), where \(A\) is a matrix, \(x\) is the vector of unknowns, and \(b\) is the output vector. This method is particularly useful for large systems where direct methods like Gaussian elimination might be computationally expensive.

Interpolative decomposition is a mathematical technique used primarily in numerical linear algebra and data analysis. It refers to a method for approximating a matrix or a function through a structured representation that allows for efficient storage and computation. The basic idea is to express a given matrix \( A \) in terms of a combination of its columns, specifically using a set of basis columns (also known as an interpolation or anchor set).

LOBPCG stands for Locally Optimal Block Preconditioned Conjugate Gradient. It is an iterative method used for the computation of a few eigenvalues and associated eigenvectors of large, sparse, symmetric (or Hermitian) matrices. The method is particularly well-suited for problems where one is interested in the smallest or largest eigenvalues of a matrix, which is common in various fields such as quantum mechanics, structural engineering, and principal component analysis.

The Jacobi method is an iterative algorithm used to solve systems of linear equations. It is particularly useful for large sparse systems, where the matrix involved has a significant number of zero elements. The method is named after the German mathematician Carl Gustav Jacob Jacobi.

SLEPc, which stands for Scalable Library for Efficient Solution of Eigenvalue problems, is a widely used library designed for solving large-scale eigenvalue problems and linear symmetric eigenvalue problems, particularly in the context of scientific and engineering applications. It is built as an extension of the Portable, Extensible Toolkit for Scientific Computation (PETSc) and focuses on harnessing high-performance computing resources to handle problems that involve massive matrices.

The Tridiagonal Matrix Algorithm (TDMA), also known as the Thomas algorithm, is a specialized algorithm used for solving systems of linear equations where the coefficient matrix is tridiagonal. A tridiagonal matrix is a matrix that has non-zero entries only on its main diagonal, and the diagonals directly above and below it.

The Al-Salam–Chihara polynomials are a family of orthogonal polynomials that arise in the theory of special functions, specifically in the context of q-series and quantum calculus. They are named after the mathematicians Abd al-Rahman Al-Salam and Jun-iti Chihara, who contributed to their study.

The Askey scheme is a classification of orthogonal polynomial sequences that arise in the context of special functions and approximation theory. Named after Richard Askey, this scheme organizes orthogonal polynomials into a hierarchy based on their properties and relationships.

Bateman polynomials, named after the mathematician Harry Bateman, are a family of orthogonal polynomials that arise in various contexts in mathematics, particularly in the theory of special functions and approximation theory. They are often denoted by \( B_n(x) \) and defined using a specific recurrence relation or via their generating functions.

The continuous dual Hahn polynomials are a family of orthogonal polynomials that arise in the context of special functions and quantum calculus. They are part of the broader family of dual Hahn polynomials and have applications in various areas, including mathematical physics, combinatorics, and approximation theory. The continuous dual Hahn polynomials can be defined in terms of a three-parameter family of polynomials, which can be specified using recurrence relations or generating functions.

Continuous dual \( q \)-Hahn polynomials are a family of orthogonal polynomials that arise in the context of basic hypergeometric series and quantum group theory. They are a part of the \( q \)-Askey scheme, which organizes various families of orthogonal polynomials based on their properties and connections to special functions.

Favard's theorem is a result in functional analysis and measure theory concerning the Fourier transforms of functions in certain spaces. Specifically, it deals with the conditions under which the Fourier transform of a function in \( L^1 \) space can be represented as a limit of averages of the values of the function.

Sobolev orthogonal polynomials are a generalization of classical orthogonal polynomials that arise in the context of Sobolev spaces. In classical approximation theory, orthogonal polynomials, such as Legendre, Hermite, and Laguerre polynomials, are orthogonal with respect to a weight function over a given interval or domain. Sobolev orthogonal polynomials extend this concept by introducing a notion of orthogonality that involves both a weight function and derivatives.

A cubic function is a type of polynomial function of degree three, which means that the highest power of the variable (usually denoted as \(x\)) is three.