We gratefully acknowledge the valuable comments of many people at the different stages of this project. We are particularly indebted to Beresford N. Parlett, who has provided invaluable comments and encouragement from the beginning.
In addition, Zhaojun Bai would like to thank Greg Ammar, Nicholas Higham, Zhongxiao Jia, G. W. Stewart, Hongguo Xu, and Qiang Ye for the fruitful discussion on the project. Part of his work was done while he was on the faculty of the Department of Mathematics, University of Kentucky. Bai and Tom Kowalski were supported in part by NSF grants ASC-9313958 and ACI-9813362 and DOE grant DE-FG03-94ER25219.
Tzu-Yi Chen was supported in part by an NSF graduate fellowship.
David Day, Rich Lehoucq, and Ross Lippert are affiliated with Sandia National Laboratories. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the U.S. Department of Energy under contract DE-AC04-94AL85000.
Jim Demmel's research was supported in part by DOE grants DE-FG03-94ER25219 and DE-FC03-98ER25351 and DOE contract W-7405-ENG-48; by NSF grants ASC-9313958 and ACI-9813361, NSF cooperative agreement ACI-9619020, and NSF Infrastructure grant EIA-9802069; and by gifts from the IBM Shared University Research Program, Sun Microsystems, and Intel. His work also utilized resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Energy Research of DOE.
Jack Dongarra would like to acknowledge the supports of NSF grants ASC-9313958 and ACI-9813362 and DOE grant DE-FG03-94ER25219 for this work.
Ren-Cang Li was supported by NSF grant ACI-9721388 and by an NSF CAREER award under grant CCR-9875201.
Xiaoye Li's work was supported by the Director, Office of Science, Division of Mathematical, Information, and Computational Sciences of the U.S. Department of Energy under contract number DE-AC03-76SF00098.
Ross Lippert and Alan Edelman would like to thank Steve Smith for many invaluable discussions. Ross Lippert and Alan Edelman were supported by NSF grant DMS-9501278.
Bo Kågström would like to acknowledge his coauthors on several papers on singular matrix pencils, namely, J. Demmel, A. Edelman, E. Elmroth, and P. Johansson.
Andrew Knyazev was partially supported by NSF grant DMS-9501507.
Axel Ruhe started his work while on sabbatical at the University of California at Berkeley, where he enjoyed the kind hospitality of Beresford N. Parlett. He received travel grants from the Swedish research councils for natural science (NFR), engineering science (TFR), and the Royal Society of Arts and Sciences in Göteborg.
Gerard Sleijpen and Henk van der Vorst were supported by the Netherlands organization for scientific research, NWO, through the Priority Program MPR, grant number 95MPR04.
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Finally, the editors thank Victor Eijkhout who helped with editing and LATEX-related issues. We are also indebted to the staff at SIAM, in particular Vickie Kearn, Deborah Poulson, Kelly Thomas, and Marianne Will for their great job of production.