Ferrandi, Giulia; Hochstenbach, Michiel E. A homogeneous Rayleigh quotient with applications in gradient methods. (English) Zbl 1522.65049 J. Comput. Appl. Math. 437, Article ID 115440, 15 p. (2024). MSC: 65F15 65F50 65K05 90C20 PDFBibTeX XMLCite \textit{G. Ferrandi} and \textit{M. E. Hochstenbach}, J. Comput. Appl. Math. 437, Article ID 115440, 15 p. (2024; Zbl 1522.65049) Full Text: DOI arXiv
Diethelm, Kai; Uhlig, Frank A new approach to shooting methods for terminal value problems of fractional differential equations. (English) Zbl 1526.65032 J. Sci. Comput. 97, No. 2, Paper No. 38, 29 p. (2023). MSC: 65L10 34A08 PDFBibTeX XMLCite \textit{K. Diethelm} and \textit{F. Uhlig}, J. Sci. Comput. 97, No. 2, Paper No. 38, 29 p. (2023; Zbl 1526.65032) Full Text: DOI arXiv OA License
Amini, Keyvan; Faramarzi, Parvaneh An adaptive modified three-term conjugate gradient method with global convergence. (English) Zbl 1527.65046 Appl. Numer. Math. 190, 187-199 (2023). MSC: 65K10 65H10 PDFBibTeX XMLCite \textit{K. Amini} and \textit{P. Faramarzi}, Appl. Numer. Math. 190, 187--199 (2023; Zbl 1527.65046) Full Text: DOI
Irwin, Brian; Haber, Eldad Secant penalized BFGS: a noise robust quasi-Newton method via penalizing the secant condition. (English) Zbl 1516.90100 Comput. Optim. Appl. 84, No. 3, 651-702 (2023). MSC: 90C30 90C53 PDFBibTeX XMLCite \textit{B. Irwin} and \textit{E. Haber}, Comput. Optim. Appl. 84, No. 3, 651--702 (2023; Zbl 1516.90100) Full Text: DOI arXiv
Danmalam, Kamaluddeen Umar; Mohammad, Hassan; Waziri, Mohammed Yusuf Structured diagonal Gauss-Newton method for nonlinear least squares. (English) Zbl 1513.65178 Comput. Appl. Math. 41, No. 2, Paper No. 68, 21 p. (2022). MSC: 65K05 90C52 90C56 PDFBibTeX XMLCite \textit{K. U. Danmalam} et al., Comput. Appl. Math. 41, No. 2, Paper No. 68, 21 p. (2022; Zbl 1513.65178) Full Text: DOI
Abdollahi, Fahimeh; Fatemi, Masoud A new conjugate gradient method based on a modified secant condition with its applications in image processing. (English) Zbl 1471.90091 RAIRO, Oper. Res. 55, No. 1, 167-187 (2021). MSC: 90C06 90C26 65Y20 PDFBibTeX XMLCite \textit{F. Abdollahi} and \textit{M. Fatemi}, RAIRO, Oper. Res. 55, No. 1, 167--187 (2021; Zbl 1471.90091) Full Text: DOI
Faramarzi, Parvaneh; Amini, Keyvan A spectral three-term Hestenes-Stiefel conjugate gradient method. (English) Zbl 1471.90138 4OR 19, No. 1, 71-92 (2021). MSC: 90C30 65K05 PDFBibTeX XMLCite \textit{P. Faramarzi} and \textit{K. Amini}, 4OR 19, No. 1, 71--92 (2021; Zbl 1471.90138) Full Text: DOI
Waziri, Mohammed Yusuf; Kufena, Muhammad Yusuf; Halilu, Abubakar Sani Derivative-free three-term spectral conjugate gradient method for symmetric nonlinear equations. (English) Zbl 1482.90248 Thai J. Math. 18, No. 3, 1417-1431 (2020). MSC: 90C52 90C30 65K05 47H10 20M12 PDFBibTeX XMLCite \textit{M. Y. Waziri} et al., Thai J. Math. 18, No. 3, 1417--1431 (2020; Zbl 1482.90248) Full Text: Link
Faramarzi, Parvaneh; Amini, Keyvan A modified conjugate gradient method based on a modified secant equation. (English) Zbl 1474.90438 J. Math. Model. 8, No. 1, 1-20 (2020). MSC: 90C30 90C06 65K05 90C53 PDFBibTeX XMLCite \textit{P. Faramarzi} and \textit{K. Amini}, J. Math. Model. 8, No. 1, 1--20 (2020; Zbl 1474.90438) Full Text: DOI
Faramarzi, Parvaneh; Amini, Keyvan A modified spectral conjugate gradient method with global convergence. (English) Zbl 1422.90053 J. Optim. Theory Appl. 182, No. 2, 667-690 (2019). MSC: 90C30 65K05 PDFBibTeX XMLCite \textit{P. Faramarzi} and \textit{K. Amini}, J. Optim. Theory Appl. 182, No. 2, 667--690 (2019; Zbl 1422.90053) Full Text: DOI
Argyros, Ioannis K.; Ren, Hongmin Enlarging the ball of convergence of secant-like methods for non-differentiable operators. (English) Zbl 1397.65081 J. Korean Math. Soc. 55, No. 1, 17-28 (2018). MSC: 65J15 45G10 47H09 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{H. Ren}, J. Korean Math. Soc. 55, No. 1, 17--28 (2018; Zbl 1397.65081) Full Text: Link
Kobayashi, Hiroshi; Narushima, Yasushi; Yabe, Hiroshi Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization. (English) Zbl 1375.90283 Optim. Methods Softw. 32, No. 6, 1313-1329 (2017). MSC: 90C30 90C06 PDFBibTeX XMLCite \textit{H. Kobayashi} et al., Optim. Methods Softw. 32, No. 6, 1313--1329 (2017; Zbl 1375.90283) Full Text: DOI
Galperin, Anatoly Iterative methods without inversion. (English) Zbl 1359.65086 Monographs and Research Notes in Mathematics. Boca Raton, FL: CRC Press (ISBN 978-1-4987-5892-5/hbk; 978-1-4987-5896-3/ebook). ix, 230 p. (2017). Reviewer: Peter P. Zabreĭko (Minsk) MSC: 65J15 65-02 47J25 45G10 65R20 PDFBibTeX XMLCite \textit{A. Galperin}, Iterative methods without inversion. Boca Raton, FL: CRC Press (2017; Zbl 1359.65086) Full Text: DOI
Babaie-Kafaki, Saman An adaptive conjugacy condition and related nonlinear conjugate gradient methods. (English) Zbl 1359.65097 Int. J. Comput. Methods 11, No. 4, Article ID 1350092, 18 p. (2014). MSC: 65K10 PDFBibTeX XMLCite \textit{S. Babaie-Kafaki}, Int. J. Comput. Methods 11, No. 4, Article ID 1350092, 18 p. (2014; Zbl 1359.65097) Full Text: DOI
Liu, Hao; Wang, Haijun; Ni, Qin On Hager and Zhang’s conjugate gradient method with guaranteed descent. (English) Zbl 1334.65111 Appl. Math. Comput. 236, 400-407 (2014). MSC: 65K10 90C52 PDFBibTeX XMLCite \textit{H. Liu} et al., Appl. Math. Comput. 236, 400--407 (2014; Zbl 1334.65111) Full Text: DOI
Shakhno, S. M.; Yarmola, H. P. On the two-step secant type method for solving nonlinear equations. (Russian. English summary) Zbl 1322.65066 Mat. Stud. 42, No. 1, 84-88 (2014). MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{S. M. Shakhno} and \textit{H. P. Yarmola}, Mat. Stud. 42, No. 1, 84--88 (2014; Zbl 1322.65066)
Babaie-Kafaki, Saman; Ghanbari, Reza Two modified three-term conjugate gradient methods with sufficient descent property. (English) Zbl 1309.90097 Optim. Lett. 8, No. 8, 2285-2297 (2014). MSC: 90C30 90C52 PDFBibTeX XMLCite \textit{S. Babaie-Kafaki} and \textit{R. Ghanbari}, Optim. Lett. 8, No. 8, 2285--2297 (2014; Zbl 1309.90097) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd Weaker convergence conditions for the secant method. (English) Zbl 1340.65109 Appl. Math., Praha 59, No. 3, 265-284 (2014). MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, Appl. Math., Praha 59, No. 3, 265--284 (2014; Zbl 1340.65109) Full Text: DOI Link
Babaie-Kafaki, Saman; Ghanbari, Reza A modified scaled conjugate gradient method with global convergence for nonconvex functions. (English) Zbl 1305.90379 Bull. Belg. Math. Soc. - Simon Stevin 21, No. 3, 465-477 (2014). MSC: 90C30 90C53 65K05 49M37 15A18 PDFBibTeX XMLCite \textit{S. Babaie-Kafaki} and \textit{R. Ghanbari}, Bull. Belg. Math. Soc. - Simon Stevin 21, No. 3, 465--477 (2014; Zbl 1305.90379) Full Text: Euclid
Babaie-Kafaki, Saman Two modified scaled nonlinear conjugate gradient methods. (English) Zbl 1278.65086 J. Comput. Appl. Math. 261, 172-182 (2014). MSC: 65K05 90C53 49M37 PDFBibTeX XMLCite \textit{S. Babaie-Kafaki}, J. Comput. Appl. Math. 261, 172--182 (2014; Zbl 1278.65086) Full Text: DOI
Babaie-Kafaki, Saman A modified scaled memoryless BFGS preconditioned conjugate gradient method for unconstrained optimization. (English) Zbl 1292.65061 4OR 11, No. 4, 361-374 (2013). MSC: 65K05 90C53 49M37 PDFBibTeX XMLCite \textit{S. Babaie-Kafaki}, 4OR 11, No. 4, 361--374 (2013; Zbl 1292.65061) Full Text: DOI
Corless, Robert M.; Fillion, Nicolas A graduate introduction to numerical methods. From the viewpoint of backward error analysis. (English) Zbl 1295.65001 New York, NY: Springer (ISBN 978-1-4614-8452-3/hbk; 978-1-4614-8453-0/ebook). xxxix, 868 p. (2013). Reviewer: Robert Plato (Siegen) MSC: 65-01 65Gxx 00A06 65Dxx 65Fxx 65T50 65Lxx 65M20 65M70 65M06 PDFBibTeX XMLCite \textit{R. M. Corless} and \textit{N. Fillion}, A graduate introduction to numerical methods. From the viewpoint of backward error analysis. New York, NY: Springer (2013; Zbl 1295.65001) Full Text: DOI
Argyros, Ioannis K.; Hilout, Saïd Directional secant-type methods for solving equations. (English) Zbl 1283.90038 J. Optim. Theory Appl. 157, No. 2, 462-485 (2013). Reviewer: Gerhard-Wilhelm Weber (Ankara) MSC: 90C30 PDFBibTeX XMLCite \textit{I. K. Argyros} and \textit{S. Hilout}, J. Optim. Theory Appl. 157, No. 2, 462--485 (2013; Zbl 1283.90038) Full Text: DOI
Griewank, Andreas Broyden updating, the good and the bad! (English) Zbl 1264.65078 Doc. Math. Extra Vol., Optimization Stories, 301-315 (2012). MSC: 65H10 PDFBibTeX XMLCite \textit{A. Griewank}, Doc. Math. Extra Vol., 301--315 (2012; Zbl 1264.65078) Full Text: EMIS
Narushima, Yasushi; Yabe, Hiroshi Conjugate gradient methods based on secant conditions that generate descent search directions for unconstrained optimization. (English) Zbl 1258.65059 J. Comput. Appl. Math. 236, No. 17, 4303-4317 (2012). Reviewer: Ctirad Matonoha (Prague) MSC: 65K05 90C30 90C06 PDFBibTeX XMLCite \textit{Y. Narushima} and \textit{H. Yabe}, J. Comput. Appl. Math. 236, No. 17, 4303--4317 (2012; Zbl 1258.65059) Full Text: DOI
Babaie-Kafaki, Saman; Ghanbari, Reza; Mahdavi-Amiri, Nezam Two new conjugate gradient methods based on modified secant equations. (English) Zbl 1202.65071 J. Comput. Appl. Math. 234, No. 5, 1374-1386 (2010). Reviewer: Vasilis Dimitriou (Chania) MSC: 65K05 PDFBibTeX XMLCite \textit{S. Babaie-Kafaki} et al., J. Comput. Appl. Math. 234, No. 5, 1374--1386 (2010; Zbl 1202.65071) Full Text: DOI
Andrei, Neculai Accelerated hybrid conjugate gradient algorithm with modified secant condition for unconstrained optimization. (English) Zbl 1192.65074 Numer. Algorithms 54, No. 1, 23-46 (2010). Reviewer: Hang Lau (Montréal) MSC: 65K05 PDFBibTeX XMLCite \textit{N. Andrei}, Numer. Algorithms 54, No. 1, 23--46 (2010; Zbl 1192.65074) Full Text: DOI
Kobayashi, Michiya; Narushima, Yasushi; Yabe, Hiroshi Nonlinear conjugate gradient methods with structured secant condition for nonlinear least squares problems. (English) Zbl 1223.65043 J. Comput. Appl. Math. 234, No. 2, 375-397 (2010). MSC: 65K05 PDFBibTeX XMLCite \textit{M. Kobayashi} et al., J. Comput. Appl. Math. 234, No. 2, 375--397 (2010; Zbl 1223.65043) Full Text: DOI
Wimmer, Harald K. Diagonal stability of matrices with cyclic structure and the secant condition. (English) Zbl 1159.93022 Syst. Control Lett. 58, No. 5, 309-313 (2009). MSC: 93D09 93C15 15A39 PDFBibTeX XMLCite \textit{H. K. Wimmer}, Syst. Control Lett. 58, No. 5, 309--313 (2009; Zbl 1159.93022) Full Text: DOI
Wu, Qingbiao; Ren, Hongmin Semilocal convergence theorem for the secant method under Mysovskii-type condition. (Chinese. English summary) Zbl 1164.65417 Chin. J. Eng. Math. 25, No. 1, 165-168 (2008). MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{Q. Wu} and \textit{H. Ren}, Chin. J. Eng. Math. 25, No. 1, 165--168 (2008; Zbl 1164.65417)
Ford, John A.; Narushima, Yasushi; Yabe, Hiroshi Multi-step nonlinear conjugate gradient methods for unconstrained minimization. (English) Zbl 1181.90221 Comput. Optim. Appl. 40, No. 2, 191-216 (2008). MSC: 90C26 90C52 PDFBibTeX XMLCite \textit{J. A. Ford} et al., Comput. Optim. Appl. 40, No. 2, 191--216 (2008; Zbl 1181.90221) Full Text: DOI
Dahlquist, Germund; Björck, Åke Numerical methods in scientific computing. Vol. 1. (English) Zbl 1153.65001 Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-0-898716-44-3/hbk; 978-0-89871-778-5/ebook). xxvii, 717 p. (2008). Reviewer: Willy Govaerts (Gent) MSC: 65-01 65H05 65Q05 65Dxx 65Gxx 65Fxx 65C05 65C10 65B05 65T50 65Hxx 65Y15 PDFBibTeX XMLCite \textit{G. Dahlquist} and \textit{Å. Björck}, Numerical methods in scientific computing. Vol. 1. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2008; Zbl 1153.65001) Full Text: DOI
Shakhno, Stepan Secant method under the generalized Lipschitz conditions for the first-order divided differences. (Ukrainian. English summary) Zbl 1199.65188 Mat. Visn. Nauk. Tov. Im. Shevchenka 4, 296-303 (2007). MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{S. Shakhno}, Mat. Visn. Nauk. Tov. Im. Shevchenka 4, 296--303 (2007; Zbl 1199.65188)
Argyros, Ioannis K. On the convergence of the secant method under the gamma condition. (English) Zbl 1141.65034 Cent. Eur. J. Math. 5, No. 2, 205-214 (2007). Reviewer: János Karátson (Budapest) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros}, Cent. Eur. J. Math. 5, No. 2, 205--214 (2007; Zbl 1141.65034) Full Text: DOI
Yabe, Hiroshi; Ogasawara, Hideho; Yoshino, Masayuki Local and superlinear convergence of quasi-Newton methods based on modified secant conditions. (English) Zbl 1124.65054 J. Comput. Appl. Math. 205, No. 1, 617-632 (2007). Reviewer: Nada Djuranović-Miličić (Belgrade) MSC: 65K05 90C30 90C53 PDFBibTeX XMLCite \textit{H. Yabe} et al., J. Comput. Appl. Math. 205, No. 1, 617--632 (2007; Zbl 1124.65054) Full Text: DOI
Chen, Jinhai; Shen, Zuhe Convergence analysis of the secant type methods. (English) Zbl 1120.65072 Appl. Math. Comput. 188, No. 1, 514-524 (2007). MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{J. Chen} and \textit{Z. Shen}, Appl. Math. Comput. 188, No. 1, 514--524 (2007; Zbl 1120.65072) Full Text: DOI
Argyros, Ioannis K. A Kantorovich-type analysis for a fast iterative method for solving nonlinear equations. (English) Zbl 1121.65061 J. Math. Anal. Appl. 332, No. 1, 97-108 (2007). Reviewer: Iulian Coroian (Baia Mare) MSC: 65J15 47J25 PDFBibTeX XMLCite \textit{I. K. Argyros}, J. Math. Anal. Appl. 332, No. 1, 97--108 (2007; Zbl 1121.65061) Full Text: DOI
Sontag, Eduardo D. Passivity gains and the “secant condition” for stability. (English) Zbl 1129.93476 Syst. Control Lett. 55, No. 3, 177-183 (2006). MSC: 93D05 93D10 93D15 93D25 PDFBibTeX XMLCite \textit{E. D. Sontag}, Syst. Control Lett. 55, No. 3, 177--183 (2006; Zbl 1129.93476) Full Text: DOI arXiv
Yabe, Hiroshi; Takano, Masahiro Global convergence properties of nonlinear conjugate gradient methods with modified secant condition. (English) Zbl 1056.90130 Comput. Optim. Appl. 28, No. 2, 203-225 (2004). MSC: 90C30 90C52 PDFBibTeX XMLCite \textit{H. Yabe} and \textit{M. Takano}, Comput. Optim. Appl. 28, No. 2, 203--225 (2004; Zbl 1056.90130) Full Text: DOI
Yabe, Hiroshi; Yamaki, Naokazu A bounded deterioration property of a symmetric positive definite class of Newton-like methods and its application. (English) Zbl 0998.90089 J. Oper. Res. Soc. Japan 42, No. 4, 373-388 (1999). MSC: 90C53 65H10 PDFBibTeX XMLCite \textit{H. Yabe} and \textit{N. Yamaki}, J. Oper. Res. Soc. Japan 42, No. 4, 373--388 (1999; Zbl 0998.90089) Full Text: DOI
Oñate, Eugenio; Matias, William T. A critical displacement approach for predicting structural instability. (English) Zbl 0883.73033 Comput. Methods Appl. Mech. Eng. 134, No. 1-2, 135-161 (1996). MSC: 74G60 74K10 74S05 PDFBibTeX XMLCite \textit{E. Oñate} and \textit{W. T. Matias}, Comput. Methods Appl. Mech. Eng. 134, No. 1--2, 135--161 (1996; Zbl 0883.73033) Full Text: DOI Link
Nievergelt, Yves The condition of Steffensen’s acceleration in several variables. (English) Zbl 0835.65074 J. Comput. Appl. Math. 58, No. 3, 291-305 (1995). Reviewer: E.L.Allgower (Fort Collins) MSC: 65H10 PDFBibTeX XMLCite \textit{Y. Nievergelt}, J. Comput. Appl. Math. 58, No. 3, 291--305 (1995; Zbl 0835.65074) Full Text: DOI
Martínez, José Mario On the global convergence of a curvilinear search method for unconstrained optimization. (English) Zbl 0807.65065 Mat. Apl. Comput. 11, No. 3, 227-236 (1992). Reviewer: F.Luban (Bucureşti) MSC: 65K05 90C30 PDFBibTeX XMLCite \textit{J. M. Martínez}, Mat. Apl. Comput. 11, No. 3, 227--236 (1992; Zbl 0807.65065)
Thron, C. D. The secant condition for instability in biochemical feedback control. I: The role of cooperativity and saturability. (English) Zbl 0751.92002 Bull. Math. Biol. 53, No. 3, 383-401 (1991). Reviewer: S.Curteanu (Iaşi) MSC: 92C45 80A30 93C95 92C40 PDFBibTeX XMLCite \textit{C. D. Thron}, Bull. Math. Biol. 53, No. 3, 383--401 (1991; Zbl 0751.92002)
Ip, Chi Ming; Todd, Michael J. Optimal conditioning and convergence in rank one quasi-Newton updates. (English) Zbl 0638.65041 SIAM J. Numer. Anal. 25, No. 1, 206-221 (1988). Reviewer: A.Pokatayev MSC: 65H10 65F35 65K05 90C30 PDFBibTeX XMLCite \textit{C. M. Ip} and \textit{M. J. Todd}, SIAM J. Numer. Anal. 25, No. 1, 206--221 (1988; Zbl 0638.65041) Full Text: DOI
Bird, W. W.; Martin, J. B. A secant approximation for holonomic elastic-plastic incremental analysis with a von Mises yield condition. (English) Zbl 0615.73031 FEMSA ’85, Finite element methods in South Afr., Proc. Conf., Stellenbosch/South Afr. 1985, 233-268 (1985). MSC: 74S30 74S05 65K10 74C99 PDFBibTeX XML