Chang, S.-L.; Chien, C.-S.; Jeng, B.-W. Tracing the solution surface with folds of a two-parameter system. (English) Zbl 1092.65503 Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, No. 8, 2689-2700 (2005). MSC: 65H20 35G15 47J15 PDFBibTeX XMLCite \textit{S. L. Chang} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 15, No. 8, 2689--2700 (2005; Zbl 1092.65503) Full Text: DOI
Gruais, I.; Cousin-Rittemard, N. M. M.; Dijkstra, H. A. A priori estimations of a global homotopy residue continuation method. (English) Zbl 1081.65120 Numer. Funct. Anal. Optimization 26, No. 4-5, 507-521 (2005). Reviewer: Luis Vazquez (Madrid) MSC: 65P30 65H20 37M20 PDFBibTeX XMLCite \textit{I. Gruais} et al., Numer. Funct. Anal. Optim. 26, No. 4--5, 507--521 (2005; Zbl 1081.65120) Full Text: DOI HAL
Gervais, Jean-Jacques; Sadiky, Hassan A continuation method based on a high order predictor and an adaptive steplength control. (English) Zbl 1056.65052 ZAMM, Z. Angew. Math. Mech. 84, No. 8, 551-563 (2004). MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{J.-J. Gervais} and \textit{H. Sadiky}, ZAMM, Z. Angew. Math. Mech. 84, No. 8, 551--563 (2004; Zbl 1056.65052) Full Text: DOI
Gould, Nicholas I. M.; Orban, Dominique; Sartenaer, Annick; Toint, Philippe L. Componentwise fast convergence in the solution of full-rank systems of nonlinear equations. (English) Zbl 1012.65046 Math. Program. 92, No. 3 (B), 481-508 (2002). Reviewer: Peter Reichensperger (Oberasbach) MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{N. I. M. Gould} et al., Math. Program. 92, No. 3 (B), 481--508 (2002; Zbl 1012.65046) Full Text: DOI Link
Hillermeier, Claus Nonlinear multiobjective optimization. A generalized homotopy approach. (English) Zbl 0966.90069 ISNM. International Series of Numerical Mathematics. 135. Basel: Birkhäuser. 135 p. (2001). Reviewer: Paulo Mbunga (Berlin) MSC: 90C29 90-02 65H20 65K05 PDFBibTeX XMLCite \textit{C. Hillermeier}, Nonlinear multiobjective optimization. A generalized homotopy approach. Basel: Birkhäuser (2001; Zbl 0966.90069)
Kotamraju, Gnana Ramdev; Akella, Maruthi Ram Stabilized continuation methods for boundary value problems. (English) Zbl 1023.65047 Appl. Math. Comput. 112, No. 2-3, 317-332 (2000). MSC: 65H10 74K10 65N38 34B15 35J65 65H20 65L10 35J05 PDFBibTeX XMLCite \textit{G. R. Kotamraju} and \textit{M. R. Akella}, Appl. Math. Comput. 112, No. 2--3, 317--332 (2000; Zbl 1023.65047) Full Text: DOI
Dent, Deborah; Paprzycki, Marcin; Kucaba-Piȩtal, Anna Recent advances in solvers for nonlinear algebraic equations. (English) Zbl 0974.65051 Comput. Assist. Mech. Eng. Sci. 7, No. 4, 793-505 (2000). Reviewer: J.Vaníček (Praha) MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{D. Dent} et al., Comput. Assist. Mech. Eng. Sci. 7, No. 4, 793--505 (2000; Zbl 0974.65051)
Böhmer, K.; Mei, Z.; Schwarzer, A.; Sebastian, Ralf Path-following of large bifurcation problems with iterative methods. (English) Zbl 0958.65062 Doedel, Eusebius (ed.) et al., Numerical methods for bifurcation problems and large-scale dynamical systems. Based on two workshops held as part of the 1997-1998 IMA academic year on emerging applications of dynamical systems. New York, NY: Springer. IMA Vol. Math. Appl. 119, 37-65 (2000). MSC: 65H17 35K57 65M06 65M60 65H20 65F10 65F15 PDFBibTeX XMLCite \textit{K. Böhmer} et al., IMA Vol. Math. Appl. 119, 37--65 (2000; Zbl 0958.65062)
Mei, Zhen Numerical bifurcation analysis for reaction-diffusion equations. (English) Zbl 0952.65105 Springer Series in Computational Mathematics. 28. Berlin: Springer. xiv, 414 p. (2000). Reviewer: Boris V.Loginov (Ul’yanovsk) MSC: 65P30 65-02 35K57 65H17 58E09 37M20 35B32 34C37 92E20 37K50 92D25 82D75 PDFBibTeX XMLCite \textit{Z. Mei}, Numerical bifurcation analysis for reaction-diffusion equations. Berlin: Springer (2000; Zbl 0952.65105)
Vasco, D. W. Regularization and trade-off associated with nonlinear geophysical inverse problems: Penalty homotopies. (English) Zbl 0913.65127 Inverse Probl. 14, No. 4, 1033-1052 (1998). Reviewer: Gabriel Dimitriu (Iaşi) MSC: 65R20 65R30 45B05 86A22 PDFBibTeX XMLCite \textit{D. W. Vasco}, Inverse Probl. 14, No. 4, 1033--1052 (1998; Zbl 0913.65127) Full Text: DOI
Rheinboldt, Werner C. Methods for solving systems of nonlinear equations. 2nd ed. (English) Zbl 0906.65051 CBMS-NSF Regional Conference Series in Applied Mathematics. 70. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. ix, 148 p. (1998). Reviewer: J.Guddat (Berlin) MSC: 65H10 65-02 65H20 65K05 90C30 PDFBibTeX XMLCite \textit{W. C. Rheinboldt}, Methods for solving systems of nonlinear equations. 2nd ed. Philadelphia, PA: SIAM (1998; Zbl 0906.65051)
Watson, Layne T.; Sosonkina, Maria; Melville, Robert C.; Morgan, Alexander P.; Walker, Homer F. Algorithm 777: HOMPACK90: A suite of Fortran 90 codes for globally convergent homotopy algorithms. (English) Zbl 0913.65042 ACM Trans. Math. Softw. 23, No. 4, 514-549 (1997). MSC: 65H20 65Y15 PDFBibTeX XMLCite \textit{L. T. Watson} et al., ACM Trans. Math. Softw. 23, No. 4, 514--549 (1997; Zbl 0913.65042) Full Text: DOI Link
Attili, Basem S. On the use of predictor-corrector continuation to trace implicitly defined curves and calculating bifurcation. (English) Zbl 0890.65048 Int. J. Comput. Math. 65, No. 1-2, 149-159 (1997). Reviewer: Xu Chengxian (Xian) MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{B. S. Attili}, Int. J. Comput. Math. 65, No. 1--2, 149--159 (1997; Zbl 0890.65048) Full Text: DOI
Demarzo, Peter M.; Eaves, B. Curtis Computing equilibria of GEI by relocalization on a Grassmann manifold. (English) Zbl 0876.90026 J. Math. Econ. 26, No. 4, 479-497 (1996). MSC: 91B50 90C90 90-08 65H20 PDFBibTeX XMLCite \textit{P. M. Demarzo} and \textit{B. C. Eaves}, J. Math. Econ. 26, No. 4, 479--497 (1996; Zbl 0876.90026) Full Text: DOI
Chien, C.-S.; Lu, N.-H.; Weng, Z.-L. Conjugate gradient methods for continuation problems. II. (English) Zbl 0857.65060 J. Comput. Appl. Math. 62, No. 2, 197-216 (1995). Reviewer: J.Vaníček (Praha) MSC: 65H17 65F15 65F10 65H20 PDFBibTeX XMLCite \textit{C. S. Chien} et al., J. Comput. Appl. Math. 62, No. 2, 197--216 (1995; Zbl 0857.65060) Full Text: DOI
Melville, R.; Mackey, D. S. A new algorithm for two-dimensional numerical continuation. (English) Zbl 0840.65037 Comput. Math. Appl. 30, No. 1, 31-46 (1995). Reviewer: W.C.Rheinboldt (Pittsburgh) MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{R. Melville} and \textit{D. S. Mackey}, Comput. Math. Appl. 30, No. 1, 31--46 (1995; Zbl 0840.65037) Full Text: DOI
Hong, Bin A manifold solver with bifurcation and symmetry. (English) Zbl 0791.65035 Allgower, Eugene L. (ed.) et al., Exploiting symmetry in applied and numerical analysis. Proceedings of the 22nd AMS-SIAM summer seminar in applied mathematics, Colorado State University, Fort Collins, CO, USA, July 26-August 1, 1992. Providence, RI: American Mathematical Society. Lect. Appl. Math. 29, 259-272 (1993). Reviewer: B.Werner (Hamburg) MSC: 65H17 65H20 PDFBibTeX XMLCite \textit{B. Hong}, Lect. Appl. Math. 29, 259--272 (1993; Zbl 0791.65035)
Forster, W. Some computational methods for systems of nonlinear equations and systems of polynomial equations. (English) Zbl 0759.65020 J. Glob. Optim. 2, No. 4, 317-356 (1992). Reviewer: W.C.Rheinboldt (Pittsburgh) MSC: 65H10 65H20 26C10 12Y05 PDFBibTeX XMLCite \textit{W. Forster}, J. Glob. Optim. 2, No. 4, 317--356 (1992; Zbl 0759.65020) Full Text: DOI
Morgan, Alexander P.; Sommese, Andrew J.; Wampler, Charles W. A power series method for computing singular solutions to nonlinear analytic systems. (English) Zbl 0756.65079 Numer. Math. 63, No. 3, 391-409 (1992). Reviewer: A.P.Morgan MSC: 65H10 65E05 65H20 PDFBibTeX XMLCite \textit{A. P. Morgan} et al., Numer. Math. 63, No. 3, 391--409 (1992; Zbl 0756.65079) Full Text: DOI EuDML
Van de Velde, Eric F.; Lorenz, Jens Adaptive data distribution for concurrent continuation. (English) Zbl 0734.65046 Numer. Math. (to appear). MSC: 65H20 65H10 65N22 65Y05 65Y20 35L50 PDFBibTeX XML Full Text: EuDML
Allison, D. C. S.; Irani, K. M.; Ribbens, C. J.; Watson, L. T. High-dimensional homotopy curve tracking on a shared-memory multiprocessor. (English) Zbl 0749.65032 J. Supercomput. 5, No. 4, 347-366 (1992). Reviewer: E.L.Allgower (Fort Collins) MSC: 65H10 65H20 65Y05 PDFBibTeX XMLCite \textit{D. C. S. Allison} et al., J. Supercomput. 5, No. 4, 347--366 (1992; Zbl 0749.65032) Full Text: DOI
Desa, Colin; Irani, Kashmira M.; Ribbens, Calvin J.; Watson, Layne T.; Walker, Homer F. Preconditioned iterative methods for homotopy curve tracking. (English) Zbl 0747.65035 SIAM J. Sci. Stat. Comput. 13, No. 1, 30-46 (1992). Reviewer: J.Vaníček (Praha) MSC: 65H20 65H10 PDFBibTeX XMLCite \textit{C. Desa} et al., SIAM J. Sci. Stat. Comput. 13, No. 1, 30--46 (1992; Zbl 0747.65035) Full Text: DOI
Van de Velde, Eric F.; Lorenz, Jens Adaptive data distribution for concurrent continuation. (English) Zbl 0755.65054 Numer. Math. 62, No. 2, 269-294 (1992). MSC: 65H20 65H10 35L50 65N22 65Y05 65Y20 PDFBibTeX XMLCite \textit{E. F. Van de Velde} and \textit{J. Lorenz}, Numer. Math. 62, No. 2, 269--294 (1992; Zbl 0755.65054) Full Text: DOI EuDML
Irani, Kashmira M.; Kamat, Manohar P.; Ribbens, Calvin J.; Walker, Homer F.; Watson, Layne T. Experiments with conjugate gradient algorithms for homotopy curve tracking. (English) Zbl 0757.65057 SIAM J. Optim. 1, No. 2, 222-251 (1991). Reviewer: Wang Zeke (Guangzhou) MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{K. M. Irani} et al., SIAM J. Optim. 1, No. 2, 222--251 (1991; Zbl 0757.65057) Full Text: DOI
Morgan, Alexander P.; Sommese, Andrew J.; Wampler, Charles W. Computing singular solutions to nonlinear analytic systems. (English) Zbl 0721.65027 Numer. Math. 58, No. 7, 669-684 (1991). Reviewer: H.Matthies (Hamburg) MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{A. P. Morgan} et al., Numer. Math. 58, No. 7, 669--684 (1991; Zbl 0721.65027) Full Text: DOI EuDML
Allgower, Eugene L.; Chien, C.-S.; Georg, Kurt; Wang, C.-F. Conjugate gradient methods for continuation problems. (English) Zbl 0753.65046 J. Comput. Appl. Math. 38, No. 1-3, 1-16 (1991). Reviewer: J.Vaníček (Praha) MSC: 65H17 65H20 65F15 65F10 65F50 PDFBibTeX XMLCite \textit{E. L. Allgower} et al., J. Comput. Appl. Math. 38, No. 1--3, 1--16 (1991; Zbl 0753.65046) Full Text: DOI
Chakraborty, A.; Allison, D. C. S.; Ribbens, C. J.; Watson, L. T. Note on unit tangent vector computation for homotopy curve tracking on a hypercube. (English) Zbl 0745.65035 Parallel Comput. 17, No. 12, 1385-1395 (1991). Reviewer: W.Zulehner (Linz) MSC: 65H20 65Y05 PDFBibTeX XMLCite \textit{A. Chakraborty} et al., Parallel Comput. 17, No. 12, 1385--1395 (1991; Zbl 0745.65035) Full Text: DOI
Watson, Layne T.; Haftka, Raphael T.; Lutze, Frederick H.; Plautt, Raymond H.; Shin, Philip Y. The application of globally convergent homotopy methods to nonlinear optimization. (English) Zbl 0745.90065 Advances in numerical partial differential equations and optimization, Proc. 5th Mex.-US Workshop, Mérida/Mex. 1989, 284-298 (1991). MSC: 90C30 90-08 65H20 90-02 90C90 PDFBibTeX XMLCite \textit{L. T. Watson} et al., in: An efficient linesearch for convex piecewise-linear/quadratic functions. . 284--298 (1991; Zbl 0745.90065)
Lundberg, Bruce N.; Poore, Aubrey B. Variable order Adams-Bashforth predictors with an error-stepsize control for continuation methods. (English) Zbl 0737.65042 SIAM J. Sci. Stat. Comput. 12, No. 3, 695-723 (1991). Reviewer: H.Ade (Mainz) MSC: 65H10 65L06 65H20 34A34 65L50 PDFBibTeX XMLCite \textit{B. N. Lundberg} and \textit{A. B. Poore}, SIAM J. Sci. Stat. Comput. 12, No. 3, 695--723 (1991; Zbl 0737.65042) Full Text: DOI
Walker, Homer F.; Watson, Layne T. Least-change secant update methods for underdetermined systems. (English) Zbl 0733.65032 SIAM J. Numer. Anal. 27, No. 5, 1227-1262 (1990). Reviewer: W.Zulehner (Linz) MSC: 65H10 65C99 65H20 PDFBibTeX XMLCite \textit{H. F. Walker} and \textit{L. T. Watson}, SIAM J. Numer. Anal. 27, No. 5, 1227--1262 (1990; Zbl 0733.65032) Full Text: DOI
Wang, Jiasong; Xia, Youshen Homotopy algorithm for solving a class of symmetric positive definite generalized eigenvalue problems. (Chinese. English summary) Zbl 0731.65024 Numer. Math., Nanjing 12, No. 2, 124-134 (1990). Reviewer: Z.Mei (Marburg) MSC: 65F15 PDFBibTeX XMLCite \textit{J. Wang} and \textit{Y. Xia}, Numer. Math., Nanjing 12, No. 2, 124--134 (1990; Zbl 0731.65024)
Allgower, Eugene L.; Georg, Kurt Numerically stable homotopy methods without an extra dimension. (English) Zbl 0723.65032 Computational solution of nonlinear systems of equations, Proc. SIAM-AMS Summer Semin., Ft. Collins/CO (USA) 1988, Lect. Appl. Math. 26, 1-13 (1990). Reviewer: B.Kearfott (Lafayette) MSC: 65H20 65H10 PDFBibTeX XML
Mejia, Raymond Interactive program for continuation of solutions of large systems of nonlinear equations. (English) Zbl 0718.65040 Computational solution of nonlinear systems of equations, Proc. SIAM-AMS Summer Semin., Ft. Collins/CO (USA) 1988, Lect. Appl. Math. 26, 429-449 (1990). Reviewer: E.Allgower (Fort Collins) MSC: 65H10 65H20 80A32 92E20 65M06 65N06 65N22 PDFBibTeX XML
Govaerts, W. Bordered augmented linear systems in numerical continuation and bifurcation. (English) Zbl 0696.65049 Numer. Math. 58, No. 4, 353-368 (1990). Reviewer: W.Govaerts MSC: 65H10 65H20 65F05 65F10 PDFBibTeX XMLCite \textit{W. Govaerts}, Numer. Math. 58, No. 4, 353--368 (1990; Zbl 0696.65049) Full Text: DOI EuDML
Morgan, Alexander P.; Watson, Layne T. A globally convergent parallel algorithm for zeros of polynomial systems. (English) Zbl 0704.65037 Nonlinear Anal., Theory Methods Appl. 13, No. 11, 1339-1350 (1989). Reviewer: K.-H.Bachmann MSC: 65H10 65H20 65Y05 PDFBibTeX XMLCite \textit{A. P. Morgan} and \textit{L. T. Watson}, Nonlinear Anal., Theory Methods Appl. 13, No. 11, 1339--1350 (1989; Zbl 0704.65037) Full Text: DOI
Watson, Layne T.; Haftka, Raphael T. Modern homotopy methods in optimization. (English) Zbl 0693.65046 Comput. Methods Appl. Mech. Eng. 74, No. 3, 289-305 (1989). Reviewer: E.Allgower MSC: 65K05 90C30 65H10 PDFBibTeX XMLCite \textit{L. T. Watson} and \textit{R. T. Haftka}, Comput. Methods Appl. Mech. Eng. 74, No. 3, 289--305 (1989; Zbl 0693.65046) Full Text: DOI Link
Watson, Layne T. Globally convergent homotopy methods: A tutorial. (English) Zbl 0689.65033 Appl. Math. Comput. 31, Spec. Issue, 369-396 (1989). Reviewer: B.Kearfott MSC: 65H10 PDFBibTeX XMLCite \textit{L. T. Watson}, Appl. Math. Comput. 31, 369--396 (1989; Zbl 0689.65033) Full Text: DOI
Allison, D. C. S.; Harimoto, S.; Watson, L. T. The granularity of parallel homotopy algorithms for polynomial systems of equations. (English) Zbl 0683.65038 Int. J. Comput. Math. 29, No. 1, 21-37 (1989). Reviewer: E.Allgower MSC: 65H10 65Y05 PDFBibTeX XMLCite \textit{D. C. S. Allison} et al., Int. J. Comput. Math. 29, No. 1, 21--37 (1989; Zbl 0683.65038) Full Text: DOI Link
Pelz, Wolfgang; Watson, Layne T. Message length effects for solving polynomial systems on a hypercube. (English) Zbl 0674.65025 Parallel Comput. 10, No. 2, 161-176 (1989). Reviewer: A.Galántai MSC: 65H10 65Y05 PDFBibTeX XMLCite \textit{W. Pelz} and \textit{L. T. Watson}, Parallel Comput. 10, No. 2, 161--176 (1989; Zbl 0674.65025) Full Text: DOI
Li, T. Y.; Rhee, N. H. Homotopy algorithm for symmetric eigenvalue problems. (English) Zbl 0653.65025 Numer. Math. 55, No. 3, 265-280 (1989). Reviewer: T.Y.Li MSC: 65F15 65Y05 PDFBibTeX XMLCite \textit{T. Y. Li} and \textit{N. H. Rhee}, Numer. Math. 55, No. 3, 265--280 (1989; Zbl 0653.65025) Full Text: DOI EuDML
Watson, Layne T.; Scott, L. Ridgway Solving Galerkin approximations to nonlinear two-point boundary value problems by a globally convergent homotopy method. (English) Zbl 0645.65043 SIAM J. Sci. Stat. Comput. 8, 768-789 (1987). Reviewer: Z.Jackiewicz MSC: 65L10 65H10 65L60 34B15 PDFBibTeX XMLCite \textit{L. T. Watson} and \textit{L. R. Scott}, SIAM J. Sci. Stat. Comput. 8, 768--789 (1987; Zbl 0645.65043) Full Text: DOI Link
Schwetlick, Hubert; Cleve, Jürgen Higher order predictors and adaptive steplength control in path following algorithms. (English) Zbl 0641.65048 SIAM J. Numer. Anal. 24, 1382-1393 (1987). Reviewer: H.Matthies MSC: 65H10 PDFBibTeX XMLCite \textit{H. Schwetlick} and \textit{J. Cleve}, SIAM J. Numer. Anal. 24, 1382--1393 (1987; Zbl 0641.65048) Full Text: DOI
Watson, Layne T.; Scott, Melvin R. Solving spline-collocation approximations to nonlinear two-point boundary-value problems by a homotopy method. (English) Zbl 0635.65099 Appl. Math. Comput. 24, 333-357 (1987). Reviewer: W.Zulehner MSC: 65L10 65H10 34B15 PDFBibTeX XMLCite \textit{L. T. Watson} and \textit{M. R. Scott}, Appl. Math. Comput. 24, 333--357 (1987; Zbl 0635.65099) Full Text: DOI Link
Watson, Layne T. Numerical linear algebra aspects of globally convergent homotopy methods. (English) Zbl 0608.65028 SIAM Rev. 28, 529-545 (1986). Reviewer: H.Matthies MSC: 65H10 65F30 PDFBibTeX XMLCite \textit{L. T. Watson}, SIAM Rev. 28, 529--545 (1986; Zbl 0608.65028) Full Text: DOI Link