TY - CHAP
T1 - On the spectrum of a nonlinear two parameter matrix eigenvalue problem
AU - Gil’, Michael
N1 - Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - We consider the nonlinear two parameter eigenvalue problem (Tp − λ1Ap1 − λ2Ap2 − λ1λ2Ap3)vp = 0, where λ1, λ2 ∈C; Tp, Apk (p = 1, 2;k = 1, 2, 3) are matrices. Bounds for the spectral radius of that problem are suggested. Our main tool is the recent norm estimates for the resolvent of an operator on the tensor product of Euclidean spaces. In addition, we investigate perturbations of the considered problem and derive a Gershgorin type bounds for the spectrum. It is shown that the main result of the paper is sharp.
AB - We consider the nonlinear two parameter eigenvalue problem (Tp − λ1Ap1 − λ2Ap2 − λ1λ2Ap3)vp = 0, where λ1, λ2 ∈C; Tp, Apk (p = 1, 2;k = 1, 2, 3) are matrices. Bounds for the spectral radius of that problem are suggested. Our main tool is the recent norm estimates for the resolvent of an operator on the tensor product of Euclidean spaces. In addition, we investigate perturbations of the considered problem and derive a Gershgorin type bounds for the spectrum. It is shown that the main result of the paper is sharp.
UR - http://www.scopus.com/inward/record.url?scp=85049298898&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-89815-5_13
DO - 10.1007/978-3-319-89815-5_13
M3 - Chapter
AN - SCOPUS:85049298898
T3 - Springer Optimization and Its Applications
SP - 387
EP - 402
BT - Springer Optimization and Its Applications
PB - Springer International Publishing
ER -