caa a22 4500 388057394 CHVBK 20180307125111.0 cr unu---uuuuu 161130e199801 xx s 000 0 eng 10.1017/S0962492900002828 doi S0962492900002828 pii (NATIONALLICENCE)cambridge-10.1017/S0962492900002828 Ipsen Ilse C. F. Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA E-mail: ipsen@math.ncsu.edu http://www4.ncsu.edu/~ipsen/info.html Relative perturbation results for matrix eigenvalues and singular values [Elektronische Daten] [Ilse C. F. Ipsen] It used to be good enough to bound absolute of matrix eigenvalues and singular values. Not any more. Now it is fashionable to bound relative errors. We present a collection of relative perturbation results which have emerged during the past ten years. No need to throw away all those absolute error bound, though. Deep down, the derivation of many relative bounds can be based on absolute bounds. This means that relative bounds are not always better. They may just be better sometimes - and exactly when depends on the perturbation. Copyright © Cambridge University Press 1998 Acta Numerica Cambridge University Press 7(1998-01), 151-201 0962-4929 7<151 1998 7 ANU https://doi.org/10.1017/S0962492900002828 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0962492900002828 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ipsen Ilse C. F. Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA E-mail: ipsen@math.ncsu.edu http://www4.ncsu.edu/~ipsen/info.html NATIONALLICENCE 773 0- Acta Numerica Cambridge University Press 7(1998-01), 151-201 0962-4929 7<151 1998 7 ANU CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge