MARC record from Internet Archive

LEADER: 01813nam 2200265 a 45 0
001 a199449
008 980625s1989 cau b f000|0 eng d
040 $aCMontNP$cCMontNP
086 0 $aD 208.14/2:NPS-53-89-015
100 1 $aGoldstein, Allen A.
245 13 $aOn calculating analytic centers /$cAllen Goldstein.
260 $aMonterey, Calif. :$bNaval Postgraduate School ;$aSpringfield, Va. :$bAvailable from National Technical Information Service,$c[1989]
300 $a7 p. ;$c28 cm.
500 $aTitle from cover.
500 $a"NPS-53-89-015."
500 $a"August 1989."
500 $aAD A215 635.
504 $aIncludes bibliographical references (p. 7).
520 $aThe analytic center of a polytope can be calculated in polynomial time by Newton's method. This note was motivated by papers of Renegar and Shub(88) and by Ye(89). We apply Smale's(86) estimates at one point for Newton's method to the problem of finding the analytic center of a polytope. The method converges globally in the appropriate norm. The ideas are then applied to obtain a possible benchmark for path following methods. When Smale's method is tractable its power stems not only from the fact that the information is concentrated at one point. There are 2 norms to estimate, not 3 as in the Kantorovich estimate. Moreover no estimate of the inverse of the derivative operator by itself is needed. The need for the norm of the inverse by itself often makes for coarse estimates. (kr)
592 $aaq/aq cc:9116 06/25/98
650 4 $aCOMPUTATIONS.
710 2 $aNaval Postgraduate School (U.S.).$bDept. of Mathematics.
740 01 $aNPS-53-89-015.
926 $aNPS-LIB$bDIGIPROJ$cD 208.14/2:NPS-53-89-015$dBOOK$eNEVER$f1
926 $aNPS-LIB$bFEDDOCS$cD 208.14/2:NPS-53-89-015$dBOOK$f2