Jan 15, 2024 · Various modifications of Newton's method have been proposed that converge quadratically at multiple roots. This chapter discusses one standard method that finds ...

Jun 4, 2024 · j is a rational multiple of another frequency, and r. 2. examples with m = 1,r = 2 x(t) = sint + sin 2t : periodic x(t) = sint + sinp2t : quasiperiodic. Page ...

Jul 7, 2024 · Therefore, the Julia set includes all the repulsive fixed points and ... multiple-root finders. Discrete Contin. Dyn. Syst. B 2020, 25, 3087–3109 ...

Feb 17, 2024 · Another example favored by Julia is found in Newton's method for finding the ... multiple dynamic attractors from different initial states of the network.

Aug 31, 2024 · 15.2 Multi-dimensional Newton's Method. In real-world applications, functions often have multiple variables, making the problem nonlinear and more complex.

Apr 18, 2024 · ≥ r, with equality only possible if n = v(d) = v(k) (in other words, if k is a multiple of pn). Since no critical point can be larger than the largest fixed ...

May 27, 2024 · In other words, the reflection of β through the hyperplane orthogonal to α is obtained by subtracting an integer multiple of α from β. Hence, the set C is a ...

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Jul 31, 2024 · The slope of this segment is at least \frac{v(d)-v(k a_k)}{d-k} \ge r, with equality only possible if n=v(d) = v(k) (in other words, if k is a multiple of p^n).

Jul 2, 2024 · real-valued function is angle-valued if it is continuous modulo 2𝜋,. i.e., real values that differ by an integer multiple of 2𝜋 encode the same angle. In ...