Smoothness [Big-Oh Bootcamp] скачать в хорошем качестве

Smoothness [Big-Oh Bootcamp]

Today we cover the topic of smoothness, a valuable analysis tool. I provide simplifying conditions that allow you to restrict the inputs to an integer power (other smoothness rules do exist, they are in my notes). I first talk a bit about asymptotically (eventually) non-decreasing functions, then smooth functions, that all smooth functions are b-smooth (a key ingredient of proving claims such as the smoothness rule I do present), and the main result. Finally, I show you how you can clean up the analysis I gave for the Harmonic Numbers example I provided elsewhere:    • Proving Harmonic Number H(n) is O(log n), ...   Note, there are separate videos proving smoothness, and the proofs of the two theorems I provide here. They will become available soon, if not available at the time of this video's upload. All smooth functions are b-smooth:    • Proving Smooth Functions are b-Smooth [Big...   Proof of Smoothness Rule:    • Proof of Smoothness Rule [Big-Oh Bootcamp]   Have a beautiful day! Supporters (to date of publication, by tier (top to bottom)): ---------------------------------------------------------- Patreon Supporters (General Support): -Draikou Patreon Supporters (Basic Support): -Tor Asbjørn Bekkelund Patreon Supporters (Special Thank You, and Supporter Access!): -Eric R -Tracy Mae ----------------------------------------------------------- Become a supporter today! To support my work and mission to provide free or accessible Computer Science education (especially in theory), subscribe to the channel, share my videos. Please donate and contribute to support my work for more content: PATREON:   / pagewizard​​   SUBSCRIBESTAR: https://www.subscribestar.com/drpage​​ PAYPAL: https://paypal.me/pagewizard​​ Follow also at: FACEBOOK:   / danielrpage​​   TWITTER:   / pagewizardgle​​   QUORA: https://www.quora.com/profile/Daniel-... Time Stamps: 0:00 Opening 0:20 Asymptotically non-decreasing functions 6:25 The game plan today! 10:12 What is a smooth function? 14:46 All smooth functions are b-smooth 19:27 Main result ("Smoothness Rule") 26:57 Example (Revisiting Harmonic Numbers) 49:20 Summary, other remarks, other "smoothness rules". #Algorithms #Analysis #BigOh