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Potra, Florian A.

An error analysis for the secant method. (English) Zbl 0465.65033

Numer. Math. 38, 427-445 (1982).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0465.65033

Cited in 3 Reviews
Cited in 14 Documents

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators

Keywords:

secant method; Banach spaces; convergence conditions; error bounds; numerical stability
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Full Text: DOI EuDML

References:

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[2] Lancaster, P.: Error analysis for the Newton-Raphson method. Numer. Math.9, 55-68 (1966) · Zbl 0173.17801 · doi:10.1007/BF02165230
[3] Miel, G.J.: Unified error analysis for Newton-type methods. Numer. Math.33, 391-396 (1979) · Zbl 0402.65038 · doi:10.1007/BF01399322
[4] Ortega, J.M., Rheinboldt, W.C.: Iterative solution of nonlinear equations in several variables. New York, London: Academic Press 1970 · Zbl 0241.65046
[5] Ostrowski, A.M.: Solution of equations in Euclidian and Banach Spaces. New York, London: Academic Press 1973 · Zbl 0304.65002
[6] Potra, F.-A.: On a modified secant method. L’Analyse num?rique et la th?orie de l’approximation,8, 203-214 (1979) · Zbl 0445.65055
[7] Potra, F.-A.: An application of the induction method of V. Pt?k to the study of Regula Falsi. Apl. Mat.26, 111-120 (1981) · Zbl 0486.65038
[8] Potra, F.-A., Pt?k, V.: Sharp error bounds for Newton’s process. Numer. Math.34, 63-72 (1980) · Zbl 0434.65034 · doi:10.1007/BF01463998
[9] Potra, F.-A., Pt?k, V.: On a class of modified Newton processes. Num. Func. Anal. Optim.2, 107-120 (1980) · Zbl 0472.65049 · doi:10.1080/01630568008816049
[10] Potra, F.-A., Pt?k, V.: A generalization of Regula Falsi. Numer. Math.36, 333-346 (1981) · Zbl 0478.65039 · doi:10.1007/BF01396659
[11] Potra, F.-A., Pt?k, V.: Nondiscrete induction and iterative procedures (to be published)
[12] Pt?k, V.: Nondiscrete mathematical induction and iterative existence proofs. Linear Algebra Appl.13, 223-236 (1976) · Zbl 0323.46005 · doi:10.1016/0024-3795(76)90098-7
[13] Pt?k, V.: Nondiscrete mathematical induction. In: General topology and its relations to modern analysis and algebra IV. Lecture Notes in Mathematics609, pp. 166-178. Berlin Heidelberg New York: Springer 1977
[14] Rokne, J.: Newton’s method under mild differentiability conditions with error analysis. Numer. Math.18, 401-412 (1972) · Zbl 0221.65084 · doi:10.1007/BF01406677
[15] Schmidt, J.W.: Eine ?bertragung der Regula Falsi auf Gleichungen in Banach R?umen, I. II. ZAMM43, 1-8, 97-110 (1963) · Zbl 0115.34002 · doi:10.1002/zamm.19630430102
[16] Schmidt, J.W.: Regula-Falsi Verfahren mit konsistenter Steigung und Majoranten Prinzip. Period. Math. Hungar.5(3), 187-193 (1974) · Zbl 0291.65017 · doi:10.1007/BF02023198
[17] Schwetlick, H.: Numerische L?sung nichtlinearer Gleichungen. Berlin: VEB, DVW (1979) · Zbl 0402.65028
[18] Sergeev, A.S.: On the method of chords (in Russian), Sibirsk. Mat. ?.2, 282-289 (1961)
[19] Ulm, S.: Majorant principle and secant method (in Russian). I.A.N. Estonskoi S.S.R., fiz. mat.3, 217-227 (1964)
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[21] Wilkinson, J.H.: The algebraic eigenvalue problem. Oxford: Clarendon Press 1965 · Zbl 0258.65037
[22] Wozniakowski, H.: Numerical stability for solving nonlinear equations. Numer. Math.27, 373-390 (1977) · Zbl 0336.65028 · doi:10.1007/BF01399601
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