000077629 001__ 77629
000077629 005__ 20180317094001.0
000077629 037__ $$aREP_WORK
000077629 245__ $$aA multi-iterate method to solve systems of nonlinear equations
000077629 269__ $$a2006
000077629 260__ $$c2006
000077629 336__ $$aReports
000077629 500__ $$aRO-060105
000077629 520__ $$aWe propose an extension of secant methods for nonlinear equations using a population of previous iterates. Contrarily to classical secant methods, where exact interpolation is used, we prefer a least squares approach to calibrate the linear model. We propose an explicit control of the numerical stability of the method. We show that our approach can lead to an update formula. In that case, we prove the local convergence of the corresponding undamped quasi-Newton method. Finally, computational comparisons with classical quasi-Newton methods highlight a significant improvement in terms of robustness and number of function evaluations. We also present numerical tests showing the robust behavior of our method in the presence of noise.
000077629 700__ $$0240563$$aBierlaire, M.$$g118332
000077629 700__ $$aCrittin, F.
000077629 700__ $$aThémans, M.
000077629 8564_ $$s305546$$uhttps://infoscience.epfl.ch/record/77629/files/Bierlaire2006_903.pdf$$zn/a
000077629 909CO $$ooai:infoscience.tind.io:77629$$preport$$pENAC
000077629 909C0 $$0252123$$pTRANSP-OR$$xU11418
000077629 937__ $$aTRANSP-OR-REPORT-2006-001
000077629 970__ $$aBierlaire2006_903/ROSO
000077629 973__ $$aEPFL$$sPUBLISHED
000077629 980__ $$aREPORT