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A maximum curvature step and geodesic displacement for nonlinear least squares descent algorithms

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(1)A maximum curvature step and geodesic displacement for nonlinear least squares descent algorithms Guy Chavent. To cite this version: Guy Chavent. A maximum curvature step and geodesic displacement for nonlinear least squares descent algorithms. [Research Report] RR-4383, INRIA. 2002. �inria-00072205�. HAL Id: inria-00072205 https://hal.inria.fr/inria-00072205 Submitted on 23 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. A maximum curvature step and geodesic displacement for nonlinear least squares descent algorithms Guy Chavent. N° 4383 Février 2002. ISSN 0249-6399. ISRN INRIA/RR--4383--FR+ENG. THÈME 4. apport de recherche.

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(9)   . Unité de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex (France) Téléphone : +33 1 39 63 55 11 — Télécopie : +33 1 39 63 53 30.

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(57)  C ®5«¯­Ç° Âb ­  D­v 4 !#%¥Z®Ÿ®£-®v«¬¢%¥  £ ­&® H ­ zÁ-§bÀ  &Á-© µ£ D «ÇÁ®£-«¬¥Z® !4 ! # *æ;« w­¢4£j¤`¥¦¢+§c¢ ¨&§c©5ª-£-«¬§c©e­ o¶ 9» 50`¿ , ,  9» +8f¿ º¸ º , $ / ‡W. >v. ;7 r =. L„ƒ. oqjD. . cf. v. ; 5DŒ= ; EGD x EGD=. ‡L. L ; X =. v. 9 D D. L ; Œ X = L  ; XŒ= L ; X =. D. 9<;  5 D = 9 ; 5 D = E D 9 ; 5>D‹= ; G E D xEGD=. L. 9 D. eV. H 9 D H P V D ]9 xeV. . UD. W. ^L. X. PN. nL. nDr. Dsr. . ìì/Ü QF{b|b{ . D xeV. U. X 6S [v. U D. Dsr. Xoa. a. .  %Dsr. . U.   . WN. . U.   M{. . PN. . W N jF; U= pcfU. `gKL j. g. B. W N jF; U=.  %L  6U. W ; q Dj =. W N j ; U=. aQW N. ; { ; q Dj ==*a. P N j ; U=. a. ;5 D =. . q Dj. c. MUD. c. „q%Dj. W ; q Dj =. „q%Dj. D H. KW. = . >v. . oW. D. LnV‹xeV. ]9 D x eV. X. H. D H. H. ; H 9 DGH. . IW. hU. U. MD‹f H RDGH. ; 5 D = E D. ; cfU D =. J. ; 5>D‹=. >v. L V. WN. 9. 

(58). W ; q%Dj = W ; q Dj =. ; 5 D = E D. >v.

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(61). W ; qDj = W ; q Dj =. c. c. }q%Dj. L. c. ; { ; q Dj = =. P ; W N jF; Uh==. c. a. P N jb; U=. Kj D. c. ;5 D =. P N jF; U=. q Dj. v. >v. W ; qDj = W T; q Dj =. jD. ; 5 D = E D v. c. c. P N jF; U=. W ; q%Dj = W T; q Dj =. q Dj. P V. jD H. qjD. c. c. LnV‹x eV. WN %v. W N jF; Uh=W N. P V. . jD. W N jF; U=. Kj D. v. jD. . S. J. q

(62). P N jF; U=. D H. W ; q=. Kj D.

(63). q. . c. . Œv. . c-f. . . . X. WN. P N j ; Uh=. . U. PN. f

(64) .   `f. . qjD. ê>=ìê;?.

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