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50 relations: Adjacency list, Adjacency matrix, ALGLIB, Algorithm, Array data structure, Associative array, Band matrix, Cholesky decomposition, Combinatorics, Computer, Computer data storage, Computer memory, Computer science, Conjugate gradient method, Data compression, Data structure, Diagonal matrix, Eigen (C++ library), Engineering, Frontal solver, Generalized minimal residual method, Graph (discrete mathematics), Graph bandwidth, Harry Markowitz, Harwell-Boeing file format, Irregular matrix, Iterative method, Logical matrix, Loose coupling, Main diagonal, Matrix (mathematics), Matrix Market exchange formats, Matrix representation, MUMPS (software), Network theory, Numerical analysis, Ordered pair, Parallel computing, Pareto principle, Partial differential equation, Portable, Extensible Toolkit for Scientific Computation, Preconditioner, Science, Skyline matrix, Sparse file, Sparse graph code, Springer Science+Business Media, Symbolic Cholesky decomposition, Tridiagonal matrix, Zero-based numbering.
Adjacency list
In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph.
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Adjacency matrix
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph.
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ALGLIB
ALGLIB is a cross-platform open source numerical analysis and data processing library.
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Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Array data structure
In computer science, an array data structure, or simply an array, is a data structure consisting of a collection of elements (values or variables), each identified by at least one array index or key.
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Associative array
In computer science, an associative array, map, symbol table, or dictionary is an abstract data type composed of a collection of (key, value) pairs, such that each possible key appears at most once in the collection.
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Band matrix
In mathematics, particularly matrix theory, a band matrix is a sparse matrix whose non-zero entries are confined to a diagonal band, comprising the main diagonal and zero or more diagonals on either side.
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Cholesky decomposition
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃ-/) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g. Monte Carlo simulations.
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Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.
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Computer
A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.
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Computer data storage
Computer data storage, often called storage or memory, is a technology consisting of computer components and recording media that are used to retain digital data.
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Computer memory
In computing, memory refers to the computer hardware integrated circuits that store information for immediate use in a computer; it is synonymous with the term "primary storage".
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Computer science
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
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Conjugate gradient method
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite.
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Data compression
In signal processing, data compression, source coding, or bit-rate reduction involves encoding information using fewer bits than the original representation.
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Data structure
In computer science, a data structure is a data organization and storage format that enables efficient access and modification.
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Diagonal matrix
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero.
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Eigen (C++ library)
Eigen is a high-level C++ library of template headers for linear algebra, matrix and vector operations, geometrical transformations, numerical solvers and related algorithms.
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Engineering
Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.
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Frontal solver
A frontal solver, due to Bruce Irons is an approach to solving sparse linear systems which is used extensively in finite element analysis.
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Generalized minimal residual method
In mathematics, the generalized minimal residual method (GMRES) is an iterative method for the numerical solution of a nonsymmetric system of linear equations.
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Graph (discrete mathematics)
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
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Graph bandwidth
In graph theory, the graph bandwidth problem is to label the n vertices vi of a graph G with distinct integers f(vi) so that the quantity \max\ is minimized (E is the edge set of G).
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Harry Markowitz
Harry Max Markowitz (born August 24, 1927) is an American economist, and a recipient of the 1989 John von Neumann Theory Prize and the 1990 Nobel Memorial Prize in Economic Sciences.
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Harwell-Boeing file format
The Harwell-Boeing file format (also known as HB format) is a file format designed to store information used to describe sparse matrices.
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Irregular matrix
An irregular matrix, or ragged matrix, is a matrix that has a different number of elements in each row.
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Iterative method
In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.
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Logical matrix
A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0,1) matrix is a matrix with entries from the Boolean domain Such a matrix can be used to represent a binary relation between a pair of finite sets.
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Loose coupling
In computing and systems design a loosely coupled system is one in which each of its components has, or makes use of, little or no knowledge of the definitions of other separate components.
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Main diagonal
In linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, or major diagonal) of a matrix A is the collection of entries A_ where i.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Matrix Market exchange formats
The Matrix Market exchange formats are a set of human readable, ASCII-based file formats designed to facilitate the exchange of matrix data.
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Matrix representation
Matrix representation is a method used by a computer language to store matrices of more than one dimension in memory.
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MUMPS (software)
MUMPS (MUltifrontal Massively Parallel sparse direct Solver) is a software application for the solution of large sparse systems of linear algebraic equations on distributed memory parallel computers.
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Network theory
Network theory is the study of graphs as a representation of either symmetric relations or asymmetric relations between discrete objects.
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Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
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Ordered pair
In mathematics, an ordered pair (a, b) is a pair of objects.
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Parallel computing
Parallel computing is a type of computation in which many calculations or the execution of processes are carried out concurrently.
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Pareto principle
The Pareto principle (also known as the 80/20 rule, the law of the vital few, or the principle of factor sparsity) states that, for many events, roughly 80% of the effects come from 20% of the causes.
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Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
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Portable, Extensible Toolkit for Scientific Computation
The Portable, Extensible Toolkit for Scientific Computation (PETSc, pronounced PET-see; the S is silent), is a suite of data structures and routines developed by Argonne National Laboratory for the scalable (parallel) solution of scientific applications modeled by partial differential equations.
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Preconditioner
In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods.
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Science
R. P. Feynman, The Feynman Lectures on Physics, Vol.1, Chaps.1,2,&3.
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Skyline matrix
In scientific computing, skyline matrix storage, or SKS, or a variable band matrix storage, or envelope storage scheme is a form of a sparse matrix storage format matrix that reduces the storage requirement of a matrix more than banded storage.
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Sparse file
In computer science, a sparse file is a type of computer file that attempts to use file system space more efficiently when the file itself is partially empty.
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Sparse graph code
A Sparse graph code is a code which is represented by a sparse graph.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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Symbolic Cholesky decomposition
In the mathematical subfield of numerical analysis the symbolic Cholesky decomposition is an algorithm used to determine the non-zero pattern for the L factors of a symmetric sparse matrix when applying the Cholesky decomposition or variants.
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Tridiagonal matrix
In linear algebra, a tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the first diagonal below this, and the first diagonal above the main diagonal.
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Zero-based numbering
Zero-based numbering or index origin.
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References
[1] https://en.wikipedia.org/wiki/Sparse_matrix
