How to Study Hard Proofs in Numerical Analysis (and Real Analysis) скачать в хорошем качестве

How to Study Hard Proofs in Numerical Analysis (and Real Analysis)

Gain skill at understanding proofs in Numerical Analysis! Continuity, differentiability, the Mean Value Theorem, and Taylor's Theorem are often necessary to use. First, we look at the proof that the recursive sequence generated by the Newton-Raphson method converges for initial estimates near the fixed point of a C^2 function f when f(p) = 0 and f'(p) is not zero. Next, we define the order of convergence for a convergent sequence (in particular, linear convergence vs quadratic convergence). In general, fixed point iteration only converges linearly. But for Newton's Method, it typically converges quadratically. The proof of this last fact requires the use of Taylor's Theorem. Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter:   / billkinneymath   🔴 Follow me on Instagram:   / billkinneymath   🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ 🔴 Desiring God website: https://www.desiringgod.org/ AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.