Argyros, Ioannis K.; George, Santhosh; Erappa, Shobha M. Extending the applicability of Newton’s and secant methods under regular smoothness. (English) Zbl 07340829 Bol. Soc. Parana. Mat. (3) 39, No. 6, 195-210 (2021). MSC: 65G99 65K10 65J15 49M15 47J25 PDF BibTeX XML Cite \textit{I. K. Argyros} et al., Bol. Soc. Parana. Mat. (3) 39, No. 6, 195--210 (2021; Zbl 07340829) Full Text: Link
Nezhadhosein, Saeed New nonlinear conjugate gradient methods based on optimal Dai-Liao parameters. (English) Zbl 07326379 J. Math. Model. 8, No. 1, 21-39 (2020). MSC: 90C30 65K05 PDF BibTeX XML Cite \textit{S. Nezhadhosein}, J. Math. Model. 8, No. 1, 21--39 (2020; Zbl 07326379) Full Text: DOI
Chukkol, Yusuf Buba; Muminov, Mukhiddin Kink wave solutions to KdV-Burgers equation with forcing term. (English) Zbl 07308184 Commun. Korean Math. Soc. 35, No. 2, 685-695 (2020). MSC: 35Q53 35Q51 35L67 35L75 35C07 35C08 PDF BibTeX XML Cite \textit{Y. B. Chukkol} and \textit{M. Muminov}, Commun. Korean Math. Soc. 35, No. 2, 685--695 (2020; Zbl 07308184) Full Text: DOI
Diao, Xinliu; Liu, Hongwei; Zhao, Ting An improved three-dimensional subspace minimization conjugate gradient method. (Chinese. English summary) Zbl 07295372 J. Jilin Univ., Sci. 58, No. 3, 470-478 (2020). MSC: 90C30 65K05 PDF BibTeX XML Cite \textit{X. Diao} et al., J. Jilin Univ., Sci. 58, No. 3, 470--478 (2020; Zbl 07295372) Full Text: DOI
Argyros, Ioannis K.; George, Santhosh Two-point methods for solving equations and systems of equations. (English) Zbl 1452.65098 Appl. Math. 47, No. 2, 255-272 (2020). MSC: 65J15 47J25 PDF BibTeX XML Cite \textit{I. K. Argyros} and \textit{S. George}, Appl. Math. 47, No. 2, 255--272 (2020; Zbl 1452.65098) Full Text: DOI
Garijo, Antonio; Jarque, Xavier The secant map applied to a real polynomial with multiple roots. (English) Zbl 1456.37105 Discrete Contin. Dyn. Syst. 40, No. 12, 6783-6794 (2020). Reviewer: Nikolay Kyurkchiev (Plovdiv) MSC: 37N30 37G35 37C70 65H04 PDF BibTeX XML Cite \textit{A. Garijo} and \textit{X. Jarque}, Discrete Contin. Dyn. Syst. 40, No. 12, 6783--6794 (2020; Zbl 1456.37105) Full Text: DOI
Balashov, M. V. Gradient projection method on matrix manifolds. (English. Russian original) Zbl 1452.90248 Comput. Math. Math. Phys. 60, No. 9, 1403-1411 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 9, 1453-1461 (2020). MSC: 90C26 PDF BibTeX XML Cite \textit{M. V. Balashov}, Comput. Math. Math. Phys. 60, No. 9, 1403--1411 (2020; Zbl 1452.90248); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 9, 1453--1461 (2020) Full Text: DOI
Diao, Xinliu; Liu, Hongwei; Liu, Zexian A new subspace minimization conjugate gradient method based on modified secant equation for unconstrained optimization. (English) Zbl 07261318 Comput. Appl. Math. 39, No. 4, Paper No. 251, 21 p. (2020). MSC: 90C30 90C06 65K05 PDF BibTeX XML Cite \textit{X. Diao} et al., Comput. Appl. Math. 39, No. 4, Paper No. 251, 21 p. (2020; Zbl 07261318) Full Text: DOI
Song, Xiongfeng; Xu, Wei; Hayami, Ken; Zheng, Ning Secant variable projection method for solving nonnegative separable least squares problems. (English) Zbl 07250899 Numer. Algorithms 85, No. 2, 737-761 (2020). MSC: 65K10 PDF BibTeX XML Cite \textit{X. Song} et al., Numer. Algorithms 85, No. 2, 737--761 (2020; Zbl 07250899) Full Text: DOI
Dehghani, Razieh; Bidabadi, Narges; Fahs, Hassan; Hosseini, Mohammad Mehdi A conjugate gradient method based on a modified secant relation for unconstrained optimization. (English) Zbl 1441.90156 Numer. Funct. Anal. Optim. 41, No. 5, 621-634 (2020). MSC: 90C30 90C53 49M37 65K05 PDF BibTeX XML Cite \textit{R. Dehghani} et al., Numer. Funct. Anal. Optim. 41, No. 5, 621--634 (2020; Zbl 1441.90156) Full Text: DOI
Lotfi, Mina; Hosseini, S. Mohammad An efficient Dai-Liao type conjugate gradient method by reformulating the CG parameter in the search direction equation. (English) Zbl 07169526 J. Comput. Appl. Math. 371, Article ID 112708, 15 p. (2020). MSC: 65 90 PDF BibTeX XML Cite \textit{M. Lotfi} and \textit{S. M. Hosseini}, J. Comput. Appl. Math. 371, Article ID 112708, 15 p. (2020; Zbl 07169526) Full Text: DOI
Chin, Wooyoung; Jung, Paul; Markowsky, Greg A note on invariance of the Cauchy and related distributions. (English) Zbl 1453.60026 Stat. Probab. Lett. 158, Article ID 108668, 6 p. (2020). MSC: 60E05 60E10 37A25 37F10 60J65 PDF BibTeX XML Cite \textit{W. Chin} et al., Stat. Probab. Lett. 158, Article ID 108668, 6 p. (2020; Zbl 1453.60026) Full Text: DOI arXiv
Dehghani, Razieh; Hosseini, Mohmadmehdi Using a modied secant equation for unconstrained optimization. (English) Zbl 1454.90113 J. Math. Ext. 13, No. 1, 103-116 (2019). MSC: 90C53 49M37 65K05 PDF BibTeX XML Cite \textit{R. Dehghani} and \textit{M. Hosseini}, J. Math. Ext. 13, No. 1, 103--116 (2019; Zbl 1454.90113) Full Text: Link
Thota, Srinivasarao A new root-finding algorithm using exponential series. (English) Zbl 1450.65044 Ural Math. J. 5, No. 1, 83-90 (2019). MSC: 65H05 PDF BibTeX XML Cite \textit{S. Thota}, Ural Math. J. 5, No. 1, 83--90 (2019; Zbl 1450.65044) Full Text: DOI MNR
Argyros, I. K.; Hernández-Verón, M. A.; Rubio, M. J. On the convergence of secant-like methods. (English) Zbl 1435.65083 Dutta, Hemen (ed.) et al., Current trends in mathematical analysis and its interdisciplinary applications. Cham: Birkhäuser. 141-183 (2019). MSC: 65J15 47J25 PDF BibTeX XML Cite \textit{I. K. Argyros} et al., in: Current trends in mathematical analysis and its interdisciplinary applications. Cham: Birkhäuser. 141--183 (2019; Zbl 1435.65083) Full Text: DOI
Argyros, Ioannis K.; George, Santhosh Local convergence analysis of two competing two-step iterative methods free of derivatives for solving equations and systems of equations. (English) Zbl 07134755 Math. Commun. 24, No. 2, 265-278 (2019). MSC: 47H09 47H10 65G99 65H10 49M15 PDF BibTeX XML Cite \textit{I. K. Argyros} and \textit{S. George}, Math. Commun. 24, No. 2, 265--278 (2019; Zbl 07134755) Full Text: Link
Rezaee, Saeed; Babaie-Kafaki, Saman An adaptive nonmonotone trust region method based on a modified scalar approximation of the Hessian in the successive quadratic subproblems. (English) Zbl 07127052 RAIRO, Oper. Res. 53, No. 3, 829-839 (2019). MSC: 65K05 90C53 49M37 PDF BibTeX XML Cite \textit{S. Rezaee} and \textit{S. Babaie-Kafaki}, RAIRO, Oper. Res. 53, No. 3, 829--839 (2019; Zbl 07127052) Full Text: DOI
Garijo, Antonio; Jarque, Xavier Global dynamics of the real secant method. (English) Zbl 1428.37099 Nonlinearity 32, No. 11, 4557-4578 (2019). MSC: 37N30 26A18 65H04 PDF BibTeX XML Cite \textit{A. Garijo} and \textit{X. Jarque}, Nonlinearity 32, No. 11, 4557--4578 (2019; Zbl 1428.37099) Full Text: DOI
Khoshgam, Zahra; Ashrafi, Ali A new hybrid conjugate gradient method for large-scale unconstrained optimization problem with non-convex objective function. (English) Zbl 1438.90270 Comput. Appl. Math. 38, No. 4, Paper No. 186, 14 p. (2019). MSC: 90C26 90C30 90C53 PDF BibTeX XML Cite \textit{Z. Khoshgam} and \textit{A. Ashrafi}, Comput. Appl. Math. 38, No. 4, Paper No. 186, 14 p. (2019; Zbl 1438.90270) Full Text: DOI
Khoshgam, Zahra; Ashrafi, Ali A new modified scaled conjugate gradient method for large-scale unconstrained optimization with non-convex objective function. (English) Zbl 1422.90023 Optim. Methods Softw. 34, No. 4, 783-796 (2019). MSC: 90C06 90C26 PDF BibTeX XML Cite \textit{Z. Khoshgam} and \textit{A. Ashrafi}, Optim. Methods Softw. 34, No. 4, 783--796 (2019; Zbl 1422.90023) Full Text: DOI
Dehghani, Razie; Hosseini, Mohammad Mehdi; Bidabadi, Narges The modified BFGS method with new secant relation for unconstrained optimization problems. (English) Zbl 1424.90257 Comput. Methods Differ. Equ. 7, No. 1, 28-41 (2019). MSC: 90C30 90C53 49M37 65K05 PDF BibTeX XML Cite \textit{R. Dehghani} et al., Comput. Methods Differ. Equ. 7, No. 1, 28--41 (2019; Zbl 1424.90257) Full Text: Link
Jain, Pankaj; Chand, Prem Bahadur; Sethi, Kriti Efficient numerical methods of Aitken type and their dynamics. (English) Zbl 07240547 Eurasian Math. J. 9, No. 3, 58-72 (2018). MSC: 65H05 PDF BibTeX XML Cite \textit{P. Jain} et al., Eurasian Math. J. 9, No. 3, 58--72 (2018; Zbl 07240547) Full Text: DOI MNR
Macías, Mauricio; Martínez, Héctor J.; Pérez, Rosana A globalized Newton type algorithm to solve the matrix quadratic equation. (Spanish. English summary) Zbl 07104537 Rev. Integr. 36, No. 2, 117-132 (2018). MSC: 65F45 15A24 PDF BibTeX XML Cite \textit{M. Macías} et al., Rev. Integr. 36, No. 2, 117--132 (2018; Zbl 07104537) Full Text: DOI
Argyros, Ioannis K.; Magreñán, Alberto; Sarría, Íñigo; Sicilia, Juan Antonio Improved convergence analysis of the secant method using restricted convergence domains with real-world applications. (English) Zbl 1438.65117 J. Nonlinear Sci. Appl. 11, No. 11, 1215-1224 (2018). MSC: 65J15 PDF BibTeX XML Cite \textit{I. K. Argyros} et al., J. Nonlinear Sci. Appl. 11, No. 11, 1215--1224 (2018; Zbl 1438.65117) Full Text: DOI
Caliciotti, Andrea; Fasano, Giovanni; Roma, Massimo Preconditioned nonlinear conjugate gradient methods based on a modified secant equation. (English) Zbl 1426.65081 Appl. Math. Comput. 318, 196-214 (2018). MSC: 65K10 65K05 90C30 90C52 PDF BibTeX XML Cite \textit{A. Caliciotti} et al., Appl. Math. Comput. 318, 196--214 (2018; Zbl 1426.65081) Full Text: DOI
Enshaei, Sharareh; Farid, Mahboubeh; Leong, Wah June; Ardestani, S. Mohsen Hashemi Higher order curvature information and its application in a modified diagonal Secant method. (English) Zbl 1416.90045 Optimization 67, No. 12, 2229-2246 (2018). MSC: 90C30 90C53 PDF BibTeX XML Cite \textit{S. Enshaei} et al., Optimization 67, No. 12, 2229--2246 (2018; Zbl 1416.90045) Full Text: DOI
Lin, Rongfei; Wu, Qingbiao; Chen, Minhong; Lei, Xuemin On the convergence ball and error analysis of the modified secant method. (English) Zbl 1405.65069 Adv. Math. Phys. 2018, Article ID 2704876, 5 p. (2018). Reviewer: Anton Iliev (Plovdiv) MSC: 65H05 PDF BibTeX XML Cite \textit{R. Lin} et al., Adv. Math. Phys. 2018, Article ID 2704876, 5 p. (2018; Zbl 1405.65069) Full Text: DOI
Argyros, Ioannis K.; Giménez, Elena; Magreñán, Á. A.; Sarría, Í.; Sicilia, Juan Antonio Improved semilocal convergence analysis in Banach space with applications to chemistry. (English) Zbl 1407.65059 J. Math. Chem. 56, No. 7, 1958-1975 (2018). MSC: 65J15 47J25 PDF BibTeX XML Cite \textit{I. K. Argyros} et al., J. Math. Chem. 56, No. 7, 1958--1975 (2018; Zbl 1407.65059) Full Text: DOI
Magreñán, Á. Alberto; Argyros, Ioannis K.; Orcos, Lara; Sicilia, Juan Antonio Secant-like methods for solving nonlinear models with applications to chemistry. (English) Zbl 1404.92229 J. Math. Chem. 56, No. 7, 1935-1957 (2018). MSC: 65J15 47J25 PDF BibTeX XML Cite \textit{Á. A. Magreñán} et al., J. Math. Chem. 56, No. 7, 1935--1957 (2018; Zbl 1404.92229) Full Text: DOI
Aliyu, M. D. S. A local iterative approach for solving the stochastic Hamilton-Jacobi-Bellman equation (SHJBE) arising in the stochastic control of affine nonlinear systems. (English) Zbl 1391.93290 Optim. Control Appl. Methods 39, No. 2, 997-1010 (2018). MSC: 93E20 90C15 93C10 60H10 PDF BibTeX XML Cite \textit{M. D. S. Aliyu}, Optim. Control Appl. Methods 39, No. 2, 997--1010 (2018; Zbl 1391.93290) 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 PDF BibTeX XML Cite \textit{I. K. Argyros} and \textit{H. Ren}, J. Korean Math. Soc. 55, No. 1, 17--28 (2018; Zbl 1397.65081) Full Text: Link
Jain, Pankaj; Sethi, Kriti Aitken type methods with high efficiency. (English) Zbl 1402.65043 Trans. A. Razmadze Math. Inst. 172, No. 2, 223-237 (2018). MSC: 65H05 PDF BibTeX XML Cite \textit{P. Jain} and \textit{K. Sethi}, Trans. A. Razmadze Math. Inst. 172, No. 2, 223--237 (2018; Zbl 1402.65043) Full Text: DOI
Cen, Zhongdi; Huang, Jian; Xu, Aimin An efficient numerical method for a two-point boundary value problem with a Caputo fractional derivative. (English) Zbl 1382.65207 J. Comput. Appl. Math. 336, 1-7 (2018). MSC: 65L10 34B05 34A08 65L70 65L20 PDF BibTeX XML Cite \textit{Z. Cen} et al., J. Comput. Appl. Math. 336, 1--7 (2018; Zbl 1382.65207) Full Text: DOI
Kumar, Abhimanyu; Gupta, D. K.; Martínez, Eulalia; Singh, Sukhjit Semilocal convergence of a Secant-type method under weak Lipschitz conditions in Banach spaces. (English) Zbl 06802862 J. Comput. Appl. Math. 330, 732-741 (2018). MSC: 65J15 PDF BibTeX XML Cite \textit{A. Kumar} et al., J. Comput. Appl. Math. 330, 732--741 (2018; Zbl 06802862) Full Text: DOI
Al-Towaiq, Mohammad H.; Abu hour, Yousef S. Two improved classes of Broyden’s methods for solving nonlinear systems of equations. (English) Zbl 1427.65073 J. Math. Comput. Sci., JMCS 17, No. 1, 22-31 (2017). MSC: 65H10 PDF BibTeX XML Cite \textit{M. H. Al-Towaiq} and \textit{Y. S. Abu hour}, J. Math. Comput. Sci., JMCS 17, No. 1, 22--31 (2017; Zbl 1427.65073) Full Text: DOI
Brach, Stella; Dormieux, Luc; Kondo, Djimedo; Vairo, Giuseppe Strength properties of nanoporous materials: a 3-layered based non-linear homogenization approach with interface effects. (English) Zbl 1423.74260 Int. J. Eng. Sci. 115, 28-42 (2017). MSC: 74F10 74Q15 74A60 PDF BibTeX XML Cite \textit{S. Brach} et al., Int. J. Eng. Sci. 115, 28--42 (2017; Zbl 1423.74260) Full Text: DOI
Kumar, Abhimanyu; Gupta, D. K.; Srivastava, Shwetabh Influence of the center condition on the two-step secant method. (English) Zbl 1405.65077 Int. J. Anal. 2017, Article ID 7364236, 9 p. (2017). Reviewer: Hang Lau (Montréal) MSC: 65J15 47J25 PDF BibTeX XML Cite \textit{A. Kumar} et al., Int. J. Anal. 2017, Article ID 7364236, 9 p. (2017; Zbl 1405.65077) Full Text: DOI
Lin, Rongfei; Wu, Qingbiao; Chen, Minhong; Liu, Lu The convergence ball and error analysis of the relaxed secant method. (English) Zbl 1405.65078 Adv. Math. Phys. 2017, Article ID 6976205, 7 p. (2017). Reviewer: Anton Iliev (Plovdiv) MSC: 65J15 47J25 PDF BibTeX XML Cite \textit{R. Lin} et al., Adv. Math. Phys. 2017, Article ID 6976205, 7 p. (2017; Zbl 1405.65078) Full Text: DOI
Anastassiou, George A.; Argyros, Ioannis K. Generalized \(g\)-fractional calculus of Canavati-type and secant-like methods. (English) Zbl 1397.65078 Int. J. Appl. Comput. Math. 3, No. 3, 1605-1617 (2017). MSC: 65J15 65H10 26A33 47J25 47J05 PDF BibTeX XML Cite \textit{G. A. Anastassiou} and \textit{I. K. Argyros}, Int. J. Appl. Comput. Math. 3, No. 3, 1605--1617 (2017; Zbl 1397.65078) Full Text: DOI
Chu, Yuanhong; Ma, Hongjuan; Zheng, Xiying The modified secant method for solving singular problem. (Chinese. English summary) Zbl 1413.65232 J. Nat. Sci. Hunan Norm. Univ. 40, No. 6, 87-92 (2017). MSC: 65J15 PDF BibTeX XML Cite \textit{Y. Chu} et al., J. Nat. Sci. Hunan Norm. Univ. 40, No. 6, 87--92 (2017; Zbl 1413.65232) Full Text: DOI
Lin, Rongfei; Wu, Qingbiao; Chen, Minhong; Khan, Yasir; Liu, Lu The convergence ball and error analysis of the two-step secant method. (English) Zbl 1413.65204 Appl. Math., Ser. B (Engl. Ed.) 32, No. 4, 397-406 (2017). MSC: 65H10 PDF BibTeX XML Cite \textit{R. Lin} et al., Appl. Math., Ser. B (Engl. Ed.) 32, No. 4, 397--406 (2017; Zbl 1413.65204) Full Text: DOI
Salimi, Mehdi; Lotfi, Taher; Sharifi, Somayeh; Siegmund, Stefan Optimal Newton-secant like methods without memory for solving nonlinear equations with its dynamics. (English) Zbl 1391.65135 Int. J. Comput. Math. 94, No. 9, 1759-1777 (2017). MSC: 65H04 65H05 PDF BibTeX XML Cite \textit{M. Salimi} et al., Int. J. Comput. Math. 94, No. 9, 1759--1777 (2017; Zbl 1391.65135) Full Text: DOI arXiv
Nik Long, N. M. A.; Salimi, Mehdi; Sharifi, Somayeh; Ferrara, Massimiliano Developing a new family of Newton-Secant method with memory based on a weight function. (English) Zbl 1382.65133 S\(\vec{\text{e}}\)MA J. 74, No. 4, 503-512 (2017). Reviewer: Anton Iliev (Plovdiv) MSC: 65H05 PDF BibTeX XML Cite \textit{N. M. A. Nik Long} et al., S\(\vec{\text{e}}\)MA J. 74, No. 4, 503--512 (2017; Zbl 1382.65133) Full Text: DOI
Ferrara, Massimiliano; Sharifi, Somayeh; Salimi, Mehdi Computing multiple zeros by using a parameter in Newton-secant method. (English) Zbl 1380.65089 S\(\vec{\text{e}}\)MA J. 74, No. 4, 361-369 (2017). MSC: 65H05 PDF BibTeX XML Cite \textit{M. Ferrara} et al., S\(\vec{\text{e}}\)MA J. 74, No. 4, 361--369 (2017; Zbl 1380.65089) Full Text: DOI arXiv
Sabi’u, Jamilu; Waziri, Mohammed Yusuf Effective modified hybrid conjugate gradient method for large-scale symmetric nonlinear equations. (English) Zbl 1390.90523 Appl. Appl. Math. 12, No. 2, 1036-1056 (2017). MSC: 90C30 90C53 65K05 49M37 15A18 PDF BibTeX XML Cite \textit{J. Sabi'u} and \textit{M. Y. Waziri}, Appl. Appl. Math. 12, No. 2, 1036--1056 (2017; Zbl 1390.90523) 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 PDF BibTeX XML Cite \textit{H. Kobayashi} et al., Optim. Methods Softw. 32, No. 6, 1313--1329 (2017; Zbl 1375.90283) Full Text: DOI
Papanikolopoulos, Stefanos; Siksek, Samir A Mordell-Weil theorem for cubic hypersurfaces of high dimension. (English) Zbl 1387.14069 Algebra Number Theory 11, No. 8, 1953-1965 (2017). Reviewer: D. R. Heath-Brown (Oxford) MSC: 14G05 11E76 11G35 11P55 PDF BibTeX XML Cite \textit{S. Papanikolopoulos} and \textit{S. Siksek}, Algebra Number Theory 11, No. 8, 1953--1965 (2017; Zbl 1387.14069) Full Text: DOI
Abdi, Fatemeh; Shakeri, Fatemeh A new descent method for symmetric non-monotone variational inequalities with application to eigenvalue complementarity problems. (English) Zbl 1376.65102 J. Optim. Theory Appl. 173, No. 3, 923-940 (2017). MSC: 65K15 90C33 49J40 49M15 PDF BibTeX XML Cite \textit{F. Abdi} and \textit{F. Shakeri}, J. Optim. Theory Appl. 173, No. 3, 923--940 (2017; Zbl 1376.65102) Full Text: DOI
Liu, Meijiao; Liu, Yong-Jin Fast algorithm for singly linearly constrained quadratic programs with box-like constraints. (English) Zbl 1365.90184 Comput. Optim. Appl. 66, No. 2, 309-326 (2017). MSC: 90C20 90C25 PDF BibTeX XML Cite \textit{M. Liu} and \textit{Y.-J. Liu}, Comput. Optim. Appl. 66, No. 2, 309--326 (2017; Zbl 1365.90184) 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 PDF BibTeX XML Cite \textit{A. Galperin}, Iterative methods without inversion. Boca Raton, FL: CRC Press (2017; Zbl 1359.65086) Full Text: DOI
Magreñán, Á. Alberto; Argyros, Ioannis K. New improved convergence analysis for the secant method. (English) Zbl 07313597 Math. Comput. Simul. 119, 161-170 (2016). MSC: 65 90 PDF BibTeX XML Cite \textit{Á. A. Magreñán} and \textit{I. K. Argyros}, Math. Comput. Simul. 119, 161--170 (2016; Zbl 07313597) Full Text: DOI
Hernández-Verón, M. A.; Rubio, M. J. On the ball of convergence of secant-like methods for non-differentiable operators. (English) Zbl 1410.65220 Appl. Math. Comput. 273, 506-512 (2016). MSC: 65J15 47J25 PDF BibTeX XML Cite \textit{M. A. Hernández-Verón} and \textit{M. J. Rubio}, Appl. Math. Comput. 273, 506--512 (2016; Zbl 1410.65220) Full Text: DOI
Godard, Roger Finding the roots of a non-linear equation: history and reliability. (English) Zbl 1408.65003 Zack, Maria (ed.) et al., Research in history and philosophy of mathematics. The CSHPM 2015 annual meeting in Washington, D. C., USA, August, 2015. Basel: Birkhäuser/Springer. Proc. Can. Soc. Hist. Philos. Math./Soc. Can. Hist. Philos. Math., 57-68 (2016). Reviewer: Nikolay Kyurkchiev (Plovdiv) MSC: 65-03 65H05 PDF BibTeX XML Cite \textit{R. Godard}, in: Research in history and philosophy of mathematics. The CSHPM 2015 annual meeting in Washington, D. C., USA, August, 2015. Basel: Birkhäuser/Springer. 57--68 (2016; Zbl 1408.65003) Full Text: DOI
Argyros, Ioannis K.; George, Santhosh Improved convergence for King-Werner-type derivative free methods. (English) Zbl 1413.65227 J. Nonlinear Anal. Optim. 7, No. 2, 97-103 (2016). MSC: 65J15 PDF BibTeX XML Cite \textit{I. K. Argyros} and \textit{S. George}, J. Nonlinear Anal. Optim. 7, No. 2, 97--103 (2016; Zbl 1413.65227) Full Text: Link
Jain, Pankaj; Bhatta, Chet Raj; Jnawali, Jivandhar Newton type iterative methods with higher order of convergence. (English) Zbl 1413.65184 J. Numer. Anal. Approx. Theory 45, No. 1, 14-26 (2016). MSC: 65H05 PDF BibTeX XML Cite \textit{P. Jain} et al., J. Numer. Anal. Approx. Theory 45, No. 1, 14--26 (2016; Zbl 1413.65184)
Wu, Xiaoxuan Research on improved Newton-type methods. (English) Zbl 1413.65193 J. Nanjing Univ., Math. Biq. 33, No. 2, 97-113 (2016). MSC: 65H05 PDF BibTeX XML Cite \textit{X. Wu}, J. Nanjing Univ., Math. Biq. 33, No. 2, 97--113 (2016; Zbl 1413.65193) Full Text: DOI
Liu, Hao; Yao, Yi; Qian, Xiaoyan; Wang, Haijun Some nonlinear conjugate gradient methods based on spectral scaling secant equations. (English) Zbl 1376.90062 Comput. Appl. Math. 35, No. 2, 639-651 (2016). MSC: 90C30 65K05 PDF BibTeX XML Cite \textit{H. Liu} et al., Comput. Appl. Math. 35, No. 2, 639--651 (2016; Zbl 1376.90062) Full Text: DOI
Améndola, Carlos; Faugère, Jean-Charles; Sturmfels, Bernd Moment varieties of Gaussian mixtures. (English) Zbl 1361.13017 J. Algebr. Stat. 7, No. 1, 14-28 (2016). MSC: 13P25 14Q15 62F10 PDF BibTeX XML Cite \textit{C. Améndola} et al., J. Algebr. Stat. 7, No. 1, 14--28 (2016; Zbl 1361.13017) Full Text: DOI arXiv
Anastassiou, George A.; Argyros, Ioannis K. A convergence analysis for secant-like methods with applications to fractional calculus. (English) Zbl 1362.65060 Panam. Math. J. 26, No. 2, 38-49 (2016). Reviewer: Bangti Jin (London) MSC: 65J15 47J25 26A33 PDF BibTeX XML Cite \textit{G. A. Anastassiou} and \textit{I. K. Argyros}, Panam. Math. J. 26, No. 2, 38--49 (2016; Zbl 1362.65060)
Wen, Ying; Li, Te; Sun, Mingwen; Zeng, Qingyuan Geometric nonlinear analysis of planar beam structures based on incremental secant stiffness. (Chinese. English summary) Zbl 1363.74086 J. Huazhong Univ. Sci. Technol. 44, No. 4, 101-105, 132 (2016). MSC: 74S30 74K10 PDF BibTeX XML Cite \textit{Y. Wen} et al., J. Huazhong Univ. Sci. Technol. 44, No. 4, 101--105, 132 (2016; Zbl 1363.74086) Full Text: DOI
Gu, Chao; Zhu, Detong Convergence of the secant algorithm for nonlinear equality and box-constrained optimization. (Chinese. English summary) Zbl 1363.90237 Chin. Ann. Math., Ser. A 37, No. 2, 191-210 (2016). MSC: 90C30 65K05 65K10 PDF BibTeX XML Cite \textit{C. Gu} and \textit{D. Zhu}, Chin. Ann. Math., Ser. A 37, No. 2, 191--210 (2016; Zbl 1363.90237) Full Text: DOI
Anastassiou, George A.; Argyros, Ioannis K. On the convergence of secant-like algorithms with applications to generalized fractional calculus. (English) Zbl 1356.65144 Appl. Math. 43, No. 2, 191-206 (2016). Reviewer: Bangti Jin (London) MSC: 65J15 47J25 26A33 PDF BibTeX XML Cite \textit{G. A. Anastassiou} and \textit{I. K. Argyros}, Appl. Math. 43, No. 2, 191--206 (2016; Zbl 1356.65144) Full Text: DOI
Kogan, Tamara; Sapir, Luba; Sapir, Amir; Sapir, Ariel The Fibonacci family of iterative processes for solving nonlinear equations. (English) Zbl 1351.65030 Appl. Numer. Math. 110, 148-158 (2016). MSC: 65H05 11B39 65Y20 PDF BibTeX XML Cite \textit{T. Kogan} et al., Appl. Numer. Math. 110, 148--158 (2016; Zbl 1351.65030) Full Text: DOI
Saha Ray, Santanu Numerical analysis with algorithms and programming. (English) Zbl 1359.65002 Boca Raton, FL: CRC Press (ISBN 978-1-4987-4174-3/hbk; 978-1-4987-4182-8/ebook). xix, 685 p. (2016). Reviewer: Hang Lau (Montréal) MSC: 65-01 68N15 65Y15 65H05 65H10 65D05 65D07 65D25 65D32 65B15 65F05 65F10 65L06 65L10 65L12 65L60 65F15 65D10 65M06 35K20 35L20 65N06 35J05 65N30 PDF BibTeX XML Cite \textit{S. Saha Ray}, Numerical analysis with algorithms and programming. Boca Raton, FL: CRC Press (2016; Zbl 1359.65002)
Argyros, Ioannis K.; Magreñán, Á. Alberto Expanding the applicability of the secant method under weaker conditions. (English) Zbl 1410.65181 Appl. Math. Comput. 266, 1000-1012 (2015). MSC: 65H10 49M15 65J15 PDF BibTeX XML Cite \textit{I. K. Argyros} and \textit{Á. A. Magreñán}, Appl. Math. Comput. 266, 1000--1012 (2015; Zbl 1410.65181) Full Text: DOI
Wang, Zhujun; Cai, Li; Zhu, Detong Line search filter inexact secant methods for nonlinear equality constrained optimization. (English) Zbl 1410.49038 Appl. Math. Comput. 263, 47-58 (2015). MSC: 49M37 65K05 90C30 PDF BibTeX XML Cite \textit{Z. Wang} et al., Appl. Math. Comput. 263, 47--58 (2015; Zbl 1410.49038) Full Text: DOI
Magreñán, Á. Alberto; Argyros, Ioannis K. New semilocal and local convergence analysis for the secant method. (English) Zbl 1410.65222 Appl. Math. Comput. 262, 298-307 (2015). MSC: 65J15 47J05 47J25 PDF BibTeX XML Cite \textit{Á. A. Magreñán} and \textit{I. K. Argyros}, Appl. Math. Comput. 262, 298--307 (2015; Zbl 1410.65222) Full Text: DOI
Argyros, I. K.; Ezquerro, J. A.; Hernández-Verón, M. A.; Hilout, S.; Magreñán, Á. A. Enlarging the convergence domain of secant-like methods for equations. (English) Zbl 1357.65064 Taiwanese J. Math. 19, No. 2, 629-652 (2015). MSC: 65J15 65H10 PDF BibTeX XML Cite \textit{I. K. Argyros} et al., Taiwanese J. Math. 19, No. 2, 629--652 (2015; Zbl 1357.65064) Full Text: DOI
Long, Haibo; Du, Jing The parallel secant method is modified to solve high order singular problems. (Chinese. English summary) Zbl 1349.65169 Math. Pract. Theory 45, No. 3, 236-241 (2015). MSC: 65H10 65Y05 PDF BibTeX XML Cite \textit{H. Long} and \textit{J. Du}, Math. Pract. Theory 45, No. 3, 236--241 (2015; Zbl 1349.65169)
Ren, Hongmin; Argyros, Ioannis K. On the convergence of King-Werner-type methods of order \(1 + \sqrt{2}\) free of derivatives. (English) Zbl 1338.65148 Appl. Math. Comput. 256, 148-159 (2015). MSC: 65J15 PDF BibTeX XML Cite \textit{H. Ren} and \textit{I. K. Argyros}, Appl. Math. Comput. 256, 148--159 (2015; Zbl 1338.65148) Full Text: DOI
Argyros, Ioannis K.; George, Santhosh Enlarging the convergence ball of the method of parabola for finding zero of derivatives. (English) Zbl 1338.65141 Appl. Math. Comput. 256, 68-74 (2015). MSC: 65J15 PDF BibTeX XML Cite \textit{I. K. Argyros} and \textit{S. George}, Appl. Math. Comput. 256, 68--74 (2015; Zbl 1338.65141) Full Text: DOI
Argyros, Ioannis K.; Cordero, Alicia; Alberto Magreñán, Á.; Torregrosa, J. R. On the convergence of a damped secant method with modified right-hand side vector. (English) Zbl 1338.65140 Appl. Math. Comput. 252, 315-323 (2015). MSC: 65J15 PDF BibTeX XML Cite \textit{I. K. Argyros} et al., Appl. Math. Comput. 252, 315--323 (2015; Zbl 1338.65140) Full Text: DOI
Jain, Pankaj; Bhatta, Chet Raj; Jnawali, Jivandhar Modified Newton type methods with higher order convergence. (English) Zbl 1336.65084 Jordan J. Math. Stat. 8, No. 4, 327-341 (2015). MSC: 65H05 PDF BibTeX XML Cite \textit{P. Jain} et al., Jordan J. Math. Stat. 8, No. 4, 327--341 (2015; Zbl 1336.65084) Full Text: Link
Jain, Divya Newton and Steffensen type methods with flexible order of convergence. (English) Zbl 1336.65083 Jordan J. Math. Stat. 8, No. 1, 43-57 (2015). MSC: 65H05 PDF BibTeX XML Cite \textit{D. Jain}, Jordan J. Math. Stat. 8, No. 1, 43--57 (2015; Zbl 1336.65083) Full Text: Link
Argyros, I. K.; Ezquerro, J. A.; Hernández, M. A.; Hilout, S.; Romero, N.; Vela, A. I. Expanding the applicability of secant-like methods for solving nonlinear equations. (English) Zbl 1349.65179 Carpathian J. Math. 31, No. 1, 11-30 (2015). MSC: 65J15 47J25 65R20 45G10 PDF BibTeX XML Cite \textit{I. K. Argyros} et al., Carpathian J. Math. 31, No. 1, 11--30 (2015; Zbl 1349.65179)
Zanni, Luca; Benfenati, Alessandro; Bertero, Mario; Ruggiero, Valeria Numerical methods for parameter estimation in Poisson data inversion. (English) Zbl 1327.65117 J. Math. Imaging Vis. 52, No. 3, 397-413 (2015). MSC: 65K05 90C25 65C60 62F10 PDF BibTeX XML Cite \textit{L. Zanni} et al., J. Math. Imaging Vis. 52, No. 3, 397--413 (2015; Zbl 1327.65117) Full Text: DOI
Tapia, Richard On averaging and representation properties of the BFGS and related secant updates. (English) Zbl 1328.49028 Math. Program. 153, No. 2 (A), 363-380 (2015). Reviewer: Guy Jumarie (Montréal) MSC: 49M15 90C53 65K05 PDF BibTeX XML Cite \textit{R. Tapia}, Math. Program. 153, No. 2 (A), 363--380 (2015; Zbl 1328.49028) Full Text: DOI
Li, Tiexiang; Huang, Wei-Qiang; Lin, Wen-Wei; Liu, Jijun On spectral analysis and a novel algorithm for transmission eigenvalue problems. (English) Zbl 1327.65227 J. Sci. Comput. 64, No. 1, 83-108 (2015). Reviewer: Vit Dolejsi (Praha) MSC: 65N25 65N30 35P15 PDF BibTeX XML Cite \textit{T. Li} et al., J. Sci. Comput. 64, No. 1, 83--108 (2015; Zbl 1327.65227) Full Text: DOI
Argyros, Ioannis K.; Magreñán, Á. Alberto Extending the convergence domain of the secant and Moser method in Banach space. (English) Zbl 1330.65081 J. Comput. Appl. Math. 290, 114-124 (2015). MSC: 65J15 47J25 PDF BibTeX XML Cite \textit{I. K. Argyros} and \textit{Á. A. Magreñán}, J. Comput. Appl. Math. 290, 114--124 (2015; Zbl 1330.65081) Full Text: DOI
Magreñán, Á. Alberto; Argyros, Ioannis K. Expanding the applicability of secant method with applications. (English) Zbl 1319.47056 Bull. Korean Math. Soc. 52, No. 3, 865-880 (2015). MSC: 47J25 49M15 65J15 PDF BibTeX XML Cite \textit{Á. A. Magreñán} and \textit{I. K. Argyros}, Bull. Korean Math. Soc. 52, No. 3, 865--880 (2015; Zbl 1319.47056) Full Text: DOI Link
Livieris, Ioannis E.; Pintelas, Panagiotis A modified Perry conjugate gradient method and its global convergence. (English) Zbl 1328.90141 Optim. Lett. 9, No. 5, 999-1015 (2015). MSC: 90C30 90C52 PDF BibTeX XML Cite \textit{I. E. Livieris} and \textit{P. Pintelas}, Optim. Lett. 9, No. 5, 999--1015 (2015; Zbl 1328.90141) Full Text: DOI
Liu, Hao; Shao, Jianfeng; Wang, Haijun; Chang, Baoxian An adaptive sizing BFGS method for unconstrained optimization. (English) Zbl 1319.65049 Calcolo 52, No. 2, 233-244 (2015). MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{H. Liu} et al., Calcolo 52, No. 2, 233--244 (2015; Zbl 1319.65049) Full Text: DOI
Wang, Zhujun; Zhu, Detong A class of improved affine-scaling interior-point secant filter methods for minimization with equality and box constraints. (English) Zbl 1318.49063 J. Appl. Math. Comput. 47, No. 1-2, 133-151 (2015). MSC: 49M37 90C51 65K05 90C30 90C55 PDF BibTeX XML Cite \textit{Z. Wang} and \textit{D. Zhu}, J. Appl. Math. Comput. 47, No. 1--2, 133--151 (2015; Zbl 1318.49063) Full Text: DOI
Zhou, Qunyan; Hang, Dan Nonmonotone adaptive trust region method with line search based on new diagonal updating. (English) Zbl 1310.65070 Appl. Numer. Math. 91, 75-88 (2015). MSC: 65K05 90C30 90C51 PDF BibTeX XML Cite \textit{Q. Zhou} and \textit{D. Hang}, Appl. Numer. Math. 91, 75--88 (2015; Zbl 1310.65070) Full Text: DOI
Argyros, I. K.; Hernández, M. A.; Hilout, S.; Romero, N. Directional Chebyshev-type methods for solving equations. (English) Zbl 1307.65072 Math. Comput. 84, No. 292, 815-830 (2015). MSC: 65J15 47J25 PDF BibTeX XML Cite \textit{I. K. Argyros} et al., Math. Comput. 84, No. 292, 815--830 (2015; Zbl 1307.65072) 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 PDF BibTeX XML Cite \textit{S. Babaie-Kafaki}, Int. J. Comput. Methods 11, No. 4, Article ID 1350092, 18 p. (2014; Zbl 1359.65097) Full Text: DOI
Amat, S.; Hernández-Verón, M. A.; Rubio, M. J. Improving the applicability of the secant method to solve nonlinear systems of equations. (English) Zbl 1338.65136 Appl. Math. Comput. 247, 741-752 (2014). MSC: 65H10 39A60 PDF BibTeX XML Cite \textit{S. Amat} et al., Appl. Math. Comput. 247, 741--752 (2014; Zbl 1338.65136) 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 PDF BibTeX XML Cite \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 PDF BibTeX XML Cite \textit{S. M. Shakhno} and \textit{H. P. Yarmola}, Mat. Stud. 42, No. 1, 84--88 (2014; Zbl 1322.65066)
Zou, Caisheng; Chen, Xiaoshan Computing the polar decomposition with a secant method. (Chinese. English summary) Zbl 1324.65060 Math. Numer. Sin. 36, No. 3, 225-230 (2014). MSC: 65F10 15A23 PDF BibTeX XML Cite \textit{C. Zou} and \textit{X. Chen}, Math. Numer. Sin. 36, No. 3, 225--230 (2014; Zbl 1324.65060)
Ezquerro, José A.; Grau, Angela; Grau-Sánchez, Miquel; Hernández-Verón, Miguel A. A new class of secant-like methods for solving nonlinear systems of equations. (English) Zbl 1311.65057 Commun. Appl. Math. Comput. Sci. 9, No. 2, 201-213 (2014). MSC: 65J15 47J25 PDF BibTeX XML Cite \textit{J. A. Ezquerro} et al., Commun. Appl. Math. Comput. Sci. 9, No. 2, 201--213 (2014; Zbl 1311.65057) Full Text: DOI
Macías C., Mauricio; Martinez, Héctor J.; Pérez, Rosana On the convergence of a secant method for nonlinear matrix equations. (Spanish. English summary) Zbl 1308.65075 Rev. Integr. 32, No. 2, 181-197 (2014). MSC: 65H10 15A24 PDF BibTeX XML Cite \textit{M. Macías C.} et al., Rev. Integr. 32, No. 2, 181--197 (2014; Zbl 1308.65075)
Argyros, Ioannis Konstantinos; Magreñán, Ángel Alberto A unified convergence analysis for secant-type methods. (English) Zbl 1320.65082 J. Korean Math. Soc. 51, No. 6, 1155-1175 (2014). Reviewer: Vasilis Dimitriou (Chania) MSC: 65J15 47J25 PDF BibTeX XML Cite \textit{I. K. Argyros} and \textit{Á. A. Magreñán}, J. Korean Math. Soc. 51, No. 6, 1155--1175 (2014; Zbl 1320.65082) 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 PDF BibTeX XML Cite \textit{I. K. Argyros} and \textit{S. Hilout}, Appl. Math., Praha 59, No. 3, 265--284 (2014; Zbl 1340.65109) Full Text: DOI
Haelterman, R.; Petit, J.; Lauwens, B.; Bruyninckx, H.; Vierendeels, J. On the non-singularity of the quasi-Newton-least squares method. (English) Zbl 1294.65057 J. Comput. Appl. Math. 257, 129-131 (2014). MSC: 65H10 65K05 90C30 90C53 PDF BibTeX XML Cite \textit{R. Haelterman} et al., J. Comput. Appl. Math. 257, 129--131 (2014; Zbl 1294.65057) Full Text: DOI
Argyros, Ioannis K.; Ren, Hongmin On the semilocal convergence of derivative free Chebyshev-Kurchatov three step method for solving equations. (English) Zbl 1306.65206 Commun. Appl. Nonlinear Anal. 21, No. 1, 55-64 (2014). Reviewer: Werner H. Schmidt (Greifswald) MSC: 65J15 47J25 PDF BibTeX XML Cite \textit{I. K. Argyros} and \textit{H. Ren}, Commun. Appl. Nonlinear Anal. 21, No. 1, 55--64 (2014; Zbl 1306.65206)
Ezquerro, J. A.; Hernández-Verón, M. A.; Rubio, M. J.; Velasco, A. I. An hybrid method that improves the accessibility of Steffensen’s method. (English) Zbl 1300.47072 Numer. Algorithms 66, No. 2, 241-267 (2014). Reviewer: Vasile Berinde (Baia Mare) MSC: 47H99 65H10 65J15 PDF BibTeX XML Cite \textit{J. A. Ezquerro} et al., Numer. Algorithms 66, No. 2, 241--267 (2014; Zbl 1300.47072) Full Text: DOI
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 PDF BibTeX XML Cite \textit{S. Babaie-Kafaki}, J. Comput. Appl. Math. 261, 172--182 (2014; Zbl 1278.65086) Full Text: DOI
Li, Junxiang; Gao, Yan; Dai, Tao; Ye, Chunming; Su, Qiang; Huo, Jiazhen Substitution secant/finite difference method to large sparse minimax problems. (English) Zbl 1281.90085 J. Ind. Manag. Optim. 10, No. 2, 637-663 (2014). MSC: 90C47 90C30 90C06 49K35 65K10 PDF BibTeX XML Cite \textit{J. Li} et al., J. Ind. Manag. Optim. 10, No. 2, 637--663 (2014; Zbl 1281.90085) Full Text: DOI
Nassif, Nabil R.; Fayyad, Dolly Khuwayri Introduction to numerical analysis and scientific computing. (English) Zbl 1281.65001 Boca Raton, FL: CRC Press (ISBN 978-1-4665-8948-3/hbk; 978-1-4665-8950-6/ebook). xix, 311 p. (2014). Reviewer: Trung Thanh Nguyen (Charlotte) MSC: 65-01 65Dxx 65C05 65L06 00A06 65H05 65F05 65Y15 PDF BibTeX XML Cite \textit{N. R. Nassif} and \textit{D. K. Fayyad}, Introduction to numerical analysis and scientific computing. Boca Raton, FL: CRC Press (2014; Zbl 1281.65001)