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A sparse matrix obtained when solving a finite element problem in two dimensions. The non-zero elements are shown in black. The non-zero elements are shown in black. In numerical analysis and scientific computing , a sparse matrix or sparse array is a matrix in which most of the elements are zero. [ 1 ]
Collaborative (joint) sparse coding: The original version of the problem is defined for a single signal . In the collaborative (joint) sparse coding model, a set of signals is available, each believed to emerge from (nearly) the same set of atoms from . In this case, the pursuit task aims to recover a set of sparse representations that best ...
A sparse matrix obtained when solving a modestly sized bundle adjustment problem. This is the arrowhead sparsity pattern of a 992×992 normal-equation (i.e. approximate Hessian) matrix. Black regions correspond to nonzero blocks.
A frontal solver is an approach to solving sparse linear systems which is used extensively in finite element analysis. [1] Algorithms of this kind are variants of Gauss elimination that automatically avoids a large number of operations involving zero terms due to the fact that the matrix is only sparse. [2]
The optimization problem is split into two sub-problems which are then solved with the conjugate gradient least squares method [19] and the simple gradient descent method respectively. The method is stopped when the desired convergence has been achieved or if the maximum number of iterations is reached.
In numerical analysis, Stone's method, also known as the strongly implicit procedure or SIP, is an algorithm for solving a sparse linear system of equations. The method uses an incomplete LU decomposition , which approximates the exact LU decomposition , to get an iterative solution of the problem.
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite. The conjugate gradient method is often implemented as an iterative algorithm , applicable to sparse systems that are too large to be handled by a direct ...
A band matrix with k 1 = k 2 = 0 is a diagonal matrix, with bandwidth 0. A band matrix with k 1 = k 2 = 1 is a tridiagonal matrix, with bandwidth 1. For k 1 = k 2 = 2 one has a pentadiagonal matrix and so on. Triangular matrices. For k 1 = 0, k 2 = n−1, one obtains the definition of an upper triangular matrix