**Author**: H.-O. Peitgen

**Publisher:** Springer

**ISBN:** 9401075239

**Category:** Science

**Page:** 226

**View:** 932

**Newton's method** has recently become one of the paradigms in the revival of Julia set theory and complex **dynamical systems**. This paper, to a large extent experimental in nature, investigates **Newton's method** for some particular model ...

**Author**: H.-O. Peitgen

**Publisher:** Springer Science & Business Media

**ISBN:** 9789400922815

**Category:** Science

**Page:** 226

**View:** 370

*Then the matrix (o) (; ;) in Newton's method is a “bordered tridiagonal' matrix of the form We now show how to solve such linear systems efficiently. 1.2.4 The Bordering Algorithm The linear systems in Newton's method for ...*

**Author**: Bernd Krauskopf

**Publisher:** Springer

**ISBN:** 9781402063565

**Category:** Science

**Page:** 399

**View:** 219

*Recall from Chapter 13 that Newton's method is an iterative procedure to solve certain equations. Given a function F, to find the solutions of F(x) = 0, we simply choose an initial guess x0 and then compute the orbit of x0 ...*

**Author**: Robert L. L. Devaney

**Publisher:** CRC Press

**ISBN:** 9781000065657

**Category:** Mathematics

**Page:** 318

**View:** 365

*We have developed this text and software for a junior-senior level course in Applicable Mathematics at Cornell University, in order to take advantage of the new qualitative and geometric insights made possible by the advent of excellent and ...*

**Author**: John H. Hubbard

**Publisher:** Springer-Verlag

**ISBN:** 9783662253687

**Category:** Mathematics

**Page:** 177

**View:** 284

*Newton's method as an iterative scheme to compute both unstable and stable fixed points of a discrete dynamical system is considered. It is shown for Newton iterations that the basins of attraction are intertwined in a complicated manner.*

**Author**: R. G. Holt

**Publisher:**

**ISBN:** OCLC:227647148

**Category:**

**Page:** 16

**View:** 113

*A First Course in Chaotic Dynamical Systems: Theory and Experiment is the first book to introduce modern topics in dynamical systems at the undergraduate level.*

**Author**: Robert L. Devaney

**Publisher:** CRC Press

**ISBN:** 9780429983115

**Category:** Mathematics

**Page:** 340

**View:** 809

*The way to solve these is to use Newton's method which we write as an iteration: An+1 || | | \n 3x3 – 3y” —6xy —1 x * – 3xy” – 1 | |||—||—|| 6xy to | 3x”y – y” | Here (xn, yn) is the nth approximation to the root.*

**Author**: Bard Ermentrout

**Publisher:** SIAM

**ISBN:** 9780898715064

**Category:** Mathematics

**Page:** 290

**View:** 584

*This book concerns the numerical simulation of dynamical systems whose trajec- ries may not be differentiable everywhere.*

**Author**: Vincent Acary

**Publisher:** Springer Science & Business Media

**ISBN:** 3540753923

**Category:** Technology & Engineering

**Page:** 525

**View:** 180

*In this section we study the theoretical aspects of these algorithms from the viewpoint of dynamical systems . We begin with a brief review of Newton's method by regarding this method as a discrete time dynamical system .*

**Author**: Christopher G. Small

**Publisher:** Oxford University Press on Demand

**ISBN:** 0198506880

**Category:** Mathematics

**Page:** 309

**View:** 123

*The authors study the Newton map $N:\mathbb{C}^2\rightarrow\mathbb{C}^2$ associated to two equations in two unknowns, as a dynamical system.*

**Author**: John H. Hubbard

**Publisher:** American Mathematical Soc.

**ISBN:** 9780821840566

**Category:** Mathematics

**Page:** 146

**View:** 680

*We solve the nonlinear system of equations using Newton's method . Each Newton step results in a linear system of equations to be solved . Because we typically consider L with many points , indirect methods will be used to solve the ...*

**Author**:

**Publisher:** Springer Science & Business Media

**ISBN:** 3540407863

**Category:**

**Page:**

**View:** 675

*Can you determine limn-2 h"(.2345)? Describe Newton's method for approximating the zeros of a function as a dynamical system. (You should be able to find Newton's method in your calculus textbook.) What is the significance of limn-co ...*

**Author**: Richard A. Holmgren

**Publisher:** Springer Science & Business Media

**ISBN:** 9781441987327

**Category:** Mathematics

**Page:** 223

**View:** 402

*Qualitative analysis of the picture leads to quantitative results and even to new mathematics. This new edition includes the latest version of the Mac Math diskette, 9.2.*

**Author**: John H. Hubbard

**Publisher:** Springer

**ISBN:** 9781461383789

**Category:** Science

**Page:** 162

**View:** 613

*5A recent collection of papers discussing Newton's method as dynamical systems is in Newton's Method and Dynamical Systems, H.-O. Peitgen (ed.), Kluver Academic Publishers, Dordrecht, 1989. See also H.-O. Peitgen P. H. Richter.*

**Author**: Heinz-Otto Peitgen

**Publisher:** Springer Science & Business Media

**ISBN:** 9780387202297

**Category:** Mathematics

**Page:** 864

**View:** 829

*... Riccati equation 71,322 maximum likelihood estimation for dynamic system 42–5 efficiency 42 optimisation methods ... 3 modified Gauss-Newton optimisation 106 modified Newton-Raphson method see Gauss-Newton method Monte-Carlo method ...*

**Author**: J.R. Raol

**Publisher:** IET

**ISBN:** 9780863413636

**Category:** Mathematics

**Page:** 388

**View:** 419