caa a22 4500 605496900 CHVBK 20210128100538.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10543-014-0519-8 doi (NATIONALLICENCE)springer-10.1007/s10543-014-0519-8 Backward perturbation analysis and residual-based error bounds for the linear response eigenvalue problem [Elektronische Daten] [Lei-Hong Zhang, Wen-Wei Lin, Ren-Cang Li] The numerical solution of a large scale linear response eigenvalue problem is often accomplished by computing a pair of deflating subspaces associated with the interesting part of the spectrum. This paper is concerned with the backward perturbation analysis for a given pair of approximate deflating subspaces or an approximate eigenquadruple. Various optimal backward perturbation bounds are obtained, as well as bounds for approximate eigenvalues computed through the pair of approximate deflating subspaces or approximate eigenquadruple. These results are reminiscent of many existing classical ones for the standard eigenvalue problem. Springer Science+Business Media Dordrecht, 2014 Linear response eigenvalue problem nationallicence Eigenvalue approximation nationallicence Rayleigh-Ritz approximation nationallicence Backward perturbation nationallicence Error bound nationallicence Deflating subspace nationallicence Zhang Lei-Hong School of Mathematics, Shanghai University of Finance and Economics, 777 Guoding Road, 200433, Shanghai, People's Republic of China aut Lin Wen-Wei Department of Applied Mathematics, National Chiao Tung University, No.1001 University Road, 30013, Hsinchu, Taiwan aut Li Ren-Cang Department of Mathematics, University of Texas at Arlington, P.O. Box 19408, 76019-0408, Arlington, TX, USA aut BIT Numerical Mathematics Springer Netherlands 55/3(2015-09-01), 869-896 0006-3835 55:3<869 2015 55 10543 https://doi.org/10.1007/s10543-014-0519-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0519-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zhang Lei-Hong School of Mathematics, Shanghai University of Finance and Economics, 777 Guoding Road, 200433, Shanghai, People's Republic of China aut NATIONALLICENCE 700 1- Lin Wen-Wei Department of Applied Mathematics, National Chiao Tung University, No.1001 University Road, 30013, Hsinchu, Taiwan aut NATIONALLICENCE 700 1- Li Ren-Cang Department of Mathematics, University of Texas at Arlington, P.O. Box 19408, 76019-0408, Arlington, TX, USA aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/3(2015-09-01), 869-896 0006-3835 55:3<869 2015 55 10543