M-Tensors and Some Applications

By Liping Zhang, Liqun Qi, Guanglu Zhou. SIAM Journal on Matrix Analysis and Applications, 2014

299 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Theory and Mathematics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/602780f233826912b0bcfc476ba5fdc9489e7266

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mathematics

1. Yaotang Li
2. Chaoqian Li
3. Yisheng Song
4. Liqun Qi
5. Haibin Chen
6. Guanglu Zhou
7. Aiquan Jiao
8. L. Caccetta

In Computational Theory and Mathematics

1. Chaoqian Li
2. Yaotang Li
3. Yisheng Song
4. Guanglu Zhou
5. Liqun Qi
6. L. Caccetta
7. Haibin Chen
8. Yiju Wang

In Radiology, Nuclear Medicine and Imaging

1. Chaoqian Li
2. Yaotang Li
3. Yisheng Song
4. Liqun Qi
5. Aiquan Jiao
6. Haibin Chen
7. Yiju Wang
8. Zhen Chen

Citations in the corpus

• Double B-tensors and quasi-double B-tensors (2014, background): “[6, 8, 34] Let A = (ai1···im) be a real tensor of order m dimension n.”
• A new eigenvalue inclusion set for tensors and its applications (2015, methodology): “Like nonnegative matrices, we can by nonnegative tensors define strong M -tensors appeared in [29], which are called nonsingular M -tensors in [30].”
• H$^+$-Eigenvalues of Laplacian and Signless Laplacian Tensors (2013, background): “M -tensors are closely related with nonnegative tensors [29].”
• Properties of Tensor Complementarity Problem and Some Classes of Structured Tensors (2014, background): “ive (semi-)definite if and only if all of its H-eigenvalues or Z-eigenvalues are positive (nonnegative) ([15, Theorem 5]). Various structured tensors were studied well. For example, Zhang, Qi and Zhou [16] and Ding, Qi and Wei [17] for Mtensors, Song and Qi [18] for P-(P0)tensors and B-(B0)tensors, Q”
• Positive Definiteness and Semi-Definiteness of Even Order Symmetric Cauchy Tensors (2014, background): “In recent years, a lot of research papers on structured tensors are presented [2, 3, 4, 8, 13, 14, 15, 17, 18, 21, 22], which studied M-tensors, circulant tensors, completely positive tensors, Hankel tensors, Hilbert tensors, P tensors and B tensors.”
• Nonsingular $H$-tensor and its criteria (2016, background): “[18, 36] establish some sufficient conditions for a square tensor to be a nonsingular M -tensor which can be applied to nonsingular H-tensors, i.”
• An even order symmetric B tensor is positive definite (2014, background): “If a Z tensor A can be written as A = cI −B, such that B is a non-negative tensor and c ≥ ρ(B), then A is called an M tensor [29].”
• Some remarks on P, P0, B and B0 tensors (2014, background): “erent from the case of m = 2 (matrices) completely. Let A∈ Tm,n. If all of the off-diagonal entries of Aare non-positive, i.e., ai1...im ≤ 0 when (i1,...,im) 6= ( i,...,i), then Ais called a Z tensor ([9]). In the following, we will show if an even order Z tensor Ais a B(B0) tensor, then Ais a P(P0) ”
• An S-type eigenvalue localization set for tensors (2015, methodology): “[5, 28] A tensor A = (ai1···im) ∈ C [m,n] is called a (strictly) diagonally dominant tensor if for i ∈ N , |ai···i| ≥ (>)ri(A).”
• Z-tensors and complementarity problems (2015, background): “−B, where r ∈ R and B is a nonnegative tensor. We say that A is an M-tensor if r ≥ ρ(B) and a strong M-tensor if r > ρ(B). The following result and its proof are modified versions of Theorem 3.3 in [25]. Proposition2.4. Let A = rI −B be a Z-tensor and µ(A) := minλ∈σ(A) Re(λ). Then, µ(A) = r −ρ(B).”