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...l can be represented in sparse [[Domain (mathematical analysis)|domain]]. "Sparse domain" refers to a domain in which only a few measurements have non-zero v ...(where <math>{M \ll N}</math>) are non-zero, then the signal is said to be sparse in that domain. ...

...oordinate-based representations of [[tensor]]s and [[sparse matrix#Storage|matrices]]. ...

...bility distribution]] over [[Sparse matrix|sparse]] [[Binary matrix|binary matrices]] with a finite number of rows and an infinite number of columns. This dist ...process is infinitely exchangeable for an [[equivalence class]] of binary matrices defined by a [[Left order topology|left-ordered]] many-to-one function. <ma ...

...thm|divide and conquer]] [[heuristic]] for the solution of [[sparse matrix|sparse]] [[symmetric matrix|symmetric]] [[System of linear equations|systems of li ...ystem of linear equations, and an edge represents a nonzero entry in the [[sparse matrix]] representing the system. ...

...roperty gives necessary and sufficient conditions on the reconstruction of sparse signals using the techniques of [[Relaxation (approximation)|<math>\ell_1</ ...neral.<ref>{{Cite journal|last=Natarajan|first=B. K.|date=1995-04-01|title=Sparse Approximate Solutions to Linear Systems|journal=SIAM J. Comput.|volume=24|i ...

...d J. Tanner "Improved Bounds on Restricted Isometry Constants for Gaussian Matrices"</ref> Web forms to evaluate bounds for the Gaussian ensemble are available ...ved by computing the exact probability that all the eigenvalues of Wishart matrices lie within an interval. ...

...|first4=J. Nathan |date=2016-05-26 |title=Inferring biological networks by sparse identification of nonlinear dynamics |class=math.DS |eprint=1605.08368}}</r ...ints in time (<math>t_1,t_2,\cdots,t_m</math>), these can be arranged into matrices of the form ...

...tain the entire matrix. Thus these techniques are suited for large, sparse matrices. The general strategy of any such colouring technique is as follows. ...remedhin, A. Tarafdar, A. Pothen, and A. Walther. Efficient Computation of Sparse Hessians Using Coloring and Automatic Differentiation". In: INFORMS J. on C ...

...means clustering]] method, and it works by iteratively alternating between sparse coding the input data based on the current dictionary, and updating the ato ...| title = K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation ...

...09">{{cite book|last=Hackbusch|first=Wolfgang|date=2015|title=Hierarchical matrices: Algorithms and Analysis|volume=49|publisher=Springer|doi=10.1007/978-3-662 ...rst2=Sergej|date=2003|title=Adaptive low-rank approximation of collocation matrices|journal=Computing|volume=70|pages=1&ndash;24|doi=10.1007/s00607-002-1469-6| ...

...(ADM<ref name=RPCA-YUAN>{{cite journal|last=X. Yuan|author2= J. Yang|title=Sparse and Low-Rank Matrix Decomposition via Alternating Direction Methods|journal ...put matrix and the sparse matrix obtained at a given iteration followed by sparse projection of the difference of the input matrix and the low-rank matrix ob ...

in [[sparse matrix]] computations (see {{harvnb|Bodlaender|Gilbert|Hafsteinsson|Kloks|1 and applied to [[sparse matrix]] computations {{harv|Schreiber|1982}}. ...

...: 869-877.</ref> In addition, PIT has applications to [[Tutte matrix|Tutte matrices]] and also to [[primality testing]], where PIT techniques led to the [[AKS ...a, Karpinski, Marek, and Singer, Michael F., "Fast Parallel Algorithms for Sparse Multivariate Polynomial Interpolation over Finite Fields", SIAM J. Comput., ...

...loped independently, most of them can be expressed as special cases of the sparse general [[Vecchia approximation]]. === Sparse covariance methods === ...

...d <math>m</math> can be solved efficiently, if the problem is sufficiently sparse. ...ns of the classic [[BFGS method]], including block-diagonal or sparse BFGS matrices. ...

[[File:Extended Sparse Matrix.png|thumb|Extended Sparse Matrix arising from a <math>10 \times 10</math> semi-separable matrix whose ...athcal{O}\left(p^2n \right)</math>, thereby making it attractive for large matrices.<ref name=":3" /> ...

...lued [[positive-definite matrix|positive-definite]] [[matrix (mathematics)|matrices]] and is the complex analog of the real [[inverse Wishart distribution]]. ...pter=On Moments of Complex Wishart and Complex Inverse Wishart Distributed Matrices|publisher=IEEE Icassp 1997|volume= 5|pages=3817–3820|doi=10.1109/ICASSP.199 ...

...k learning]]. Ideas of feature and group selection can also be extended to matrices, and these can be generalized to the nonparametric case of [[multiple kerne ...product is the [[Frobenius inner product]]. For different applications the matrices <math>X_i</math> will have different forms,<ref name="Notes">{{cite book |f ...

...|issn=0178-4617}}</ref> This data structure offers efficient operations on sparse simplicial complexes. For dense or maximal simplices, Skeleton-Blocker<ref> ...structures for simplicial [[complex representation]], their operations on sparse data are considered state-of-art. Here, we give the bounds of different use ...

...</math>, the alternative dictionary structure adopted by the convolutional sparse coding model allows the sparsity prior to be applied '''locally''' instead ...posium on Image Analysis and Interpretation (SSIAI) |chapter=Convolutional sparse representation of color images |pages=57–60 |date=6–8 March 2016 |doi=10.11 ...