![]() Travaux de l’Institut des Mathématiques Steklov XXVIII, 104–144 (1949) Kantorovich, L.: Sur la méthode de Newton. Hirsch, M., Pugh, C., Shub, M.: Invariant Manifolds. Goldstine, H.: A History of Numerical Analysis from the 16th Through the 19th Century. 235, 1515–1522 (2011)įerreira, O.P., Svaiter, B.F.: Kantorovich’s theorem on Newton’s method on Riemannian manifolds. 29, 746–759 (2009)įerreira, O.P.: Local convergence of Newton’s method under majorant condition. La Gaceta de la RSME 13, 53–76 (2010)įerreira, O.P.: Local convergence of Newton’s method in Banach space from the viewpoint of the majorant principle. 20, 303–353 (1998)Įzquerro, J., Gutiérrez, J., Hernandez, M., Romero, N., Rubio, M.-J.: El metodo de Newton: de Newton a Kantorovich. Prentice Hall, Englewood Cliffs (1983)Įdelman, A., Arias, T., Smith, S.: The geometry of algorithms with orthogonality constraints. 23, 395–419 (2003)ĭennis, J., Schnabel, R.: Numerical Methods for Unconstrained Optimization and Nonlinear Equation. 69, 1099–1115 (2000)ĭedieu, J.-P., Priouret, P., Malajovich, G.: Newton’s method on Riemannian manifolds: covariant alpha theory. 69, 1071–1098 (2000)ĭedieu, J.-P., Shub, M.: Newton’s method for overdetermined systems of equations. Springer, Berlin/New York (2006)ĭedieu, J.-P., Kim, M.-H.: Newton’s Method for Analytic Systems of Equations with Constant Rank Derivatives. Springer, New York (1997)ĭedieu, J.-P.: Points Fixes, Zéros et la Méthode de Newton. 15, 243–252 (1966)īeyn, W.-J.: On smoothness and invariance properties of the Gauss-Newton method. 10, 555–563 (2005)īen-Israel, A.: A Newton-Raphson method for the solution of systems of equations. Springer, New York/London (2008)Īrgyros, I., Gutiérrez, J.: A unified approach for enlarging the radius of convergence for Newton’s method and applications. 8, 197–226 (2008)Īrgyros, I.: Convergence and Applications of Newton-Type Iterations. Springer, Berlin/New York (1990)Īlvarez, F., Bolte, J., Munier, J.: A unifying local convergence result for Newton’s method in Riemannian manifolds. 22, 1–32 (2002)Īllgower, E., Georg, K.: Numerical Continuation Methods. Princeton University Press, Princeton/Woodstock (2008)Īdler, R., Dedieu, J.-P., Martens, M., Shub, M.: Newton’s method on Riemannian manifolds with an application to a human spine model. The routine will continue iterating until the convergence criteria are satisfied or the iteration limit is reached.Absil, P.-A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. The convergence criteria formulas are evaluated and compared against the user's inputted convergence criteria value. The user's inputted initial guess is plugged into the Newton's Method formula and the new x value is calculated. Inside the JS code that powers this calculator is the same routine outlined throughout this lesson. Since this calculator relies only on JS to perform calculations, it can provide instant solutions to the user. ![]() ![]() JS runs inside an internet browser just like a program runs inside a computer's operating system. The HTML builds the framework of the calculator, the CSS styles the framework, and the JS enables interactions with the user and the calculations to happen. This calculator is written in the web programming technologies HTML, CSS, and JavaScript (JS). The standard equation form for an ellipse is given as: ![]() The Earth's elliptical orbit (white) and an asteroid's elliptical orbit (blue) around the Sun.Īll objects in orbit around the Sun have an elliptical orbit, where the size and shape of the ellipse are unique to each respective astronomical object. One of the many real-world uses for Newton’s Method is calculating if an asteroid will encounter the Earth during its orbit around the Sun. ![]()
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