Geršgorin And His Circles

By R. Varga. 2004

739 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5e620e656e8131a53d383443ee709a07ed2d2a17

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In Geometry and Topology

Citations in the corpus

Adaptation, Learning, and Optimization over Networks (2014, background): “Gershgorin’s Theorem The second result, known as Gershgorin’s Theorem [48, 94, 101, 104, 113, 254, 264], specifies circular regions within which the eigenvalues of a matrix are located.”
A new eigenvalue inclusion set for tensors and its applications (2015, background): “If m = 2, then Theorem 8 reduces to the boundary theorem of Taussky for matrices; see [24].”
An eigenvalue localization set for tensors with applications to determine the positive (semi-)definiteness of tensors (2016, background): “In [1], Qi gave an eigenvalue localization set for real symmetric tensors, which is a generalization of the well-known Geršgorin’s eigenvalue localization set of matrices.[31,32] This result can be easily generalized to general tensors.”
Toeplitz Compressed Sensing Matrices With Applications to Sparse Channel Estimation (2010, background): “There are many valid references—see, for example, [20].”
Subspace Pursuit for Compressive Sensing: Closing the Gap Between Performance and Complexity (2008, methodology): “For OMP techniques to operate successfully, one requires that the correlation between all pairs of columns of Φ is at most 1/2K [9], which by the Gershgorin Circle Theorem [10], represents a more restrictive constraint than the RIP.”
On the eigenvalues of quaternion matrices (2011, background): “3), respectively, with 1⁄4C (for more results on the developments of Geršgorin theory; see [6,10,11,17,21,22]).”
Subspace Pursuit for Compressive Sensing Signal Reconstruction (2008, neutral): “It has provable reconstruction capability comparable to that of LP methods, and exhibits the low reconstruction complexity of matching pursuit techniques for very sparse signals.”
Convex Optimization & Euclidean Distance Geometry (2004, background): “1] [251] For p∈R+ given A=[Aij]∈ S, then all eigenvalues of A belong to the union of m closed intervals on the real line;”
Spectra of Graphs (2011, methodology): “A book-length treatment was given by Varga [363].”
An S-type eigenvalue localization set for tensors (2015, background): “In [20], Qi gave an eigenvalue localization set for real symmetric tensors, which is a generalization of the well-known Geršgorin’s eigenvalue localization set of matrices [6, 23].”
Toward Controlling Discrimination in Online Ad Auctions (2019, background): “2 in [48]) For any matrix A ∈ Rn×n, and any eigen-value λ ∈ R of A, λ ≤ max i∈[n] ∑ j∈[n] |Aij |.”
A new Brauer-type eigenvalue localization set for tensors (2016, background): “extended the Brauer’s eigenvalue localization set of matrices [7,9] to give the following Brauer-type eigenvalue localization set for tensors.”
Z-EIGENVALUE INCLUSION THEOREMS FOR TENSORS (2016, background): “When m = 2, exact eigenvalue inclusion theorems can be found in [18].”