Newton's method (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Newton's method" in English language version.

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Ostrowski, A. M. (1973). Solution of equations in Euclidean and Banach spaces. Pure and Applied Mathematics. Vol. 9 (Third edition of 1960 original ed.). New York–London: Academic Press. MR 0359306. Zbl 0304.65002.
Traub, J. F. (1964). Iterative methods for the solution of equations. Prentice-Hall Series in Automatic Computation. Englewood Cliffs, NJ: Prentice-Hall, Inc. MR 0169356. Zbl 0121.11204.
Hamilton, Richard S. (1982). "The inverse function theorem of Nash and Moser". Bulletin of the American Mathematical Society. New Series. 7 (1): 65–222. doi:10.1090/s0273-0979-1982-15004-2. MR 0656198. Zbl 0499.58003.
Gromov, Mikhael (1986). Partial differential relations. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 9. Berlin: Springer-Verlag. doi:10.1007/978-3-662-02267-2. ISBN 3-540-12177-3. MR 0864505.
Boyd, Stephen; Vandenberghe, Lieven (2004). Convex optimization. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511804441. ISBN 0-521-83378-7. MR 2061575. Zbl 1058.90049.

archive.org

Raphson, Joseph (1697). Analysis Æequationum Universalis (in Latin) (2nd ed.). London: Thomas Bradyll. doi:10.3931/e-rara-13516.
Burden, Burton; Fairs, J. Douglas; Reunolds, Albert C (July 1981). Numerical Analysis (2nd ed.). Boston, MA, United States: Prindle, Weber & Schmidt. pp. 448–452. ISBN 0-87150-314-X. OCLC 1036752194.
Evans, Gwynne A. (1995). Practical Numerical Analysis. Chichester: John Wiley & Sons. pp. 30–33. ISBN 0471955353. OCLC 1319419671.
Demidovich, Boris Pavlovich; Maron, Isaak Abramovich (1981). Computational Mathematics (Third ed.). Moscow: MIR Publishers. pp. 460–478. ISBN 9780828507042.
Stoer, Josef; Bulirsch, Roland (1980). Introduction to numerical analysis. p. 279. OCLC 1244842246.

books.google.com

Guicciardini, Niccolò (2009). Isaac Newton on Mathematical Certainty and Method. Transformations. Cambridge, Mass: MIT Press. pp. 158–159. ISBN 978-0-262-01317-8. OCLC 282968643.
Ryaben'kii, Victor S.; Tsynkov, Semyon V. (2006), A Theoretical Introduction to Numerical Analysis, CRC Press, p. 243, ISBN 9781584886075.

cambridge.org

Kiusalaas, Jaan (March 2013). Numerical Methods in Engineering with Python 3 (3rd ed.). New York: Cambridge University Press. pp. 175–176. ISBN 978-1-107-03385-6.

doi.org

Fowler, David; Robson, Eleanor (1998). "Square root approximations in Old Babylonian mathematics: YBC 7289 in context". Historia Mathematica. 25 (4): 366–378. doi:10.1006/hmat.1998.2209.
Ypma, Tjalling J. (1995). "Historical Development of the Newton-Raphson Method". SIAM Review. 37 (4): 531–551. doi:10.1137/1037125. ISSN 0036-1445. JSTOR 2132904.
Cajori, Florian (1911). "Historical Note on the Newton-Raphson Method of Approximation". The American Mathematical Monthly. 18 (2): 29–32. doi:10.2307/2973939. ISSN 0002-9890. JSTOR 2973939.
Ypma, Tjalling J. (1995). "Historical Development of the Newton-Raphson Method". SIAM Review. 37 (4): 531–551. doi:10.1137/1037125. ISSN 0036-1445. JSTOR 2132904.
Wallis, John (1685). A Treatise of Algebra, both Historical and Practical. Oxford: Richard Davis. doi:10.3931/e-rara-8842.
Raphson, Joseph (1697). Analysis Æequationum Universalis (in Latin) (2nd ed.). London: Thomas Bradyll. doi:10.3931/e-rara-13516.
Strang, Gilbert (January 1991). "A chaotic search for $i$ ". The College Mathematics Journal. 22 (1): 3–12. doi:10.2307/2686733. JSTOR 2686733.
McMullen, Curt (1987). "Families of rational maps and iterative root-finding algorithms" (PDF). Annals of Mathematics. Second Series. 125 (3): 467–493. doi:10.2307/1971408. JSTOR 1971408.
Hubbard, John; Schleicher, Dierk; Sutherland, Scott (October 2001). "How to find all roots of complex polynomials by Newton's method". Inventiones Mathematicae. 146 (1): 1–33. Bibcode:2001InMat.146....1H. doi:10.1007/s002220100149. ISSN 0020-9910. S2CID 12603806.
Hamilton, Richard S. (1982). "The inverse function theorem of Nash and Moser". Bulletin of the American Mathematical Society. New Series. 7 (1): 65–222. doi:10.1090/s0273-0979-1982-15004-2. MR 0656198. Zbl 0499.58003.
Gromov, Mikhael (1986). Partial differential relations. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 9. Berlin: Springer-Verlag. doi:10.1007/978-3-662-02267-2. ISBN 3-540-12177-3. MR 0864505.
Murota, Kazuo (1982). "Global Convergence of a Modified Newton Iteration for Algebraic Equations". SIAM Journal on Numerical Analysis. 19 (4): 793–799. Bibcode:1982SJNA...19..793M. doi:10.1137/0719055.
Boyd, Stephen; Vandenberghe, Lieven (2004). Convex optimization. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511804441. ISBN 0-521-83378-7. MR 2061575. Zbl 1058.90049.

dx.doi.org

Hubbard, John; Schleicher, Dierk; Sutherland, Scott (October 2001). "How to find all roots of complex polynomials by Newton's method". Inventiones Mathematicae. 146 (1): 1–33. Bibcode:2001InMat.146....1H. doi:10.1007/s002220100149. ISSN 0020-9910. S2CID 12603806.

e-rara.ch

Wallis, John (1685). A Treatise of Algebra, both Historical and Practical. Oxford: Richard Davis. doi:10.3931/e-rara-8842.

emis.de

Rajković, Predrag M.; Stanković, Miomir S.; Marinković, Slađana D. (2002). "Mean value theorems in $q$-calculus". Matematicki Vesnik. 54 (3–4): 171–178.

fullerton.edu

mathfaculty.fullerton.edu

"Accelerated and Modified Newton Methods". Archived from the original on 24 May 2019. Retrieved 4 March 2016.

harvard.edu

ui.adsabs.harvard.edu

Hubbard, John; Schleicher, Dierk; Sutherland, Scott (October 2001). "How to find all roots of complex polynomials by Newton's method". Inventiones Mathematicae. 146 (1): 1–33. Bibcode:2001InMat.146....1H. doi:10.1007/s002220100149. ISSN 0020-9910. S2CID 12603806.
Murota, Kazuo (1982). "Global Convergence of a Modified Newton Iteration for Algebraic Equations". SIAM Journal on Numerical Analysis. 19 (4): 793–799. Bibcode:1982SJNA...19..793M. doi:10.1137/0719055.

dash.harvard.edu

McMullen, Curt (1987). "Families of rational maps and iterative root-finding algorithms" (PDF). Annals of Mathematics. Second Series. 125 (3): 467–493. doi:10.2307/1971408. JSTOR 1971408.

jstor.org

Ypma, Tjalling J. (1995). "Historical Development of the Newton-Raphson Method". SIAM Review. 37 (4): 531–551. doi:10.1137/1037125. ISSN 0036-1445. JSTOR 2132904.
Cajori, Florian (1911). "Historical Note on the Newton-Raphson Method of Approximation". The American Mathematical Monthly. 18 (2): 29–32. doi:10.2307/2973939. ISSN 0002-9890. JSTOR 2973939.
Ypma, Tjalling J. (1995). "Historical Development of the Newton-Raphson Method". SIAM Review. 37 (4): 531–551. doi:10.1137/1037125. ISSN 0036-1445. JSTOR 2132904.
Strang, Gilbert (January 1991). "A chaotic search for $i$ ". The College Mathematics Journal. 22 (1): 3–12. doi:10.2307/2686733. JSTOR 2686733.
McMullen, Curt (1987). "Families of rational maps and iterative root-finding algorithms" (PDF). Annals of Mathematics. Second Series. 125 (3): 467–493. doi:10.2307/1971408. JSTOR 1971408.

nrbook.com

apps.nrbook.com

Press et al. 2007 Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. (2007). "Chapter 9. Root Finding and Nonlinear Sets of Equations Importance Sampling". Numerical Recipes: The Art of Scientific Computing (3rd ed.). New York: Cambridge Univ. Press. ISBN 978-0-521-88068-8.. See especially Sections 9.4, 9.6, and 9.7.

semanticscholar.org

api.semanticscholar.org

Hubbard, John; Schleicher, Dierk; Sutherland, Scott (October 2001). "How to find all roots of complex polynomials by Newton's method". Inventiones Mathematicae. 146 (1): 1–33. Bibcode:2001InMat.146....1H. doi:10.1007/s002220100149. ISSN 0020-9910. S2CID 12603806.

st-andrews.ac.uk

mathshistory.st-andrews.ac.uk

"Takakazu Seki - Biography". Maths History. Retrieved 27 November 2024.

web.archive.org

"Accelerated and Modified Newton Methods". Archived from the original on 24 May 2019. Retrieved 4 March 2016.

worldcat.org

search.worldcat.org

Ypma, Tjalling J. (1995). "Historical Development of the Newton-Raphson Method". SIAM Review. 37 (4): 531–551. doi:10.1137/1037125. ISSN 0036-1445. JSTOR 2132904.
Cajori, Florian (1911). "Historical Note on the Newton-Raphson Method of Approximation". The American Mathematical Monthly. 18 (2): 29–32. doi:10.2307/2973939. ISSN 0002-9890. JSTOR 2973939.
Guicciardini, Niccolò (2009). Isaac Newton on Mathematical Certainty and Method. Transformations. Cambridge, Mass: MIT Press. pp. 158–159. ISBN 978-0-262-01317-8. OCLC 282968643.
Ypma, Tjalling J. (1995). "Historical Development of the Newton-Raphson Method". SIAM Review. 37 (4): 531–551. doi:10.1137/1037125. ISSN 0036-1445. JSTOR 2132904.
Burden, Burton; Fairs, J. Douglas; Reunolds, Albert C (July 1981). Numerical Analysis (2nd ed.). Boston, MA, United States: Prindle, Weber & Schmidt. pp. 448–452. ISBN 0-87150-314-X. OCLC 1036752194.
Evans, Gwynne A. (1995). Practical Numerical Analysis. Chichester: John Wiley & Sons. pp. 30–33. ISBN 0471955353. OCLC 1319419671.
Hubbard, John; Schleicher, Dierk; Sutherland, Scott (October 2001). "How to find all roots of complex polynomials by Newton's method". Inventiones Mathematicae. 146 (1): 1–33. Bibcode:2001InMat.146....1H. doi:10.1007/s002220100149. ISSN 0020-9910. S2CID 12603806.
Stoer, Josef; Bulirsch, Roland (1980). Introduction to numerical analysis. p. 279. OCLC 1244842246.

zbmath.org

Ostrowski, A. M. (1973). Solution of equations in Euclidean and Banach spaces. Pure and Applied Mathematics. Vol. 9 (Third edition of 1960 original ed.). New York–London: Academic Press. MR 0359306. Zbl 0304.65002.
Traub, J. F. (1964). Iterative methods for the solution of equations. Prentice-Hall Series in Automatic Computation. Englewood Cliffs, NJ: Prentice-Hall, Inc. MR 0169356. Zbl 0121.11204.
Hamilton, Richard S. (1982). "The inverse function theorem of Nash and Moser". Bulletin of the American Mathematical Society. New Series. 7 (1): 65–222. doi:10.1090/s0273-0979-1982-15004-2. MR 0656198. Zbl 0499.58003.
Boyd, Stephen; Vandenberghe, Lieven (2004). Convex optimization. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511804441. ISBN 0-521-83378-7. MR 2061575. Zbl 1058.90049.