LatestMachine LearningCubic Roots-Fit a Quadratic Between a Turning Point And Midpoint! 0 like November 16, 2024Share this postAuthor(s): Greg Oliver Originally published on Towards AI. A Root Approximation Tool Kit Mixing and Matching Polynomial ArchitecturesGenetic Cubic Architectural DimensionsThis member-only story is on us. Upgrade to access all of Medium.This post presents a novel Cubic-Quadratic function matchup for finding Cubic roots. It exploits the little publicised fact that the Midpoint between 2 adjacent roots of a reduced Cubic when multiplied by -2 gives us the 3rd root!This is related to the sum of the factors = Coefficient B of x. In the example B=0 being a reduced Cubic.Besides being graphically intuitive the adopted Quadratic function greatly simplifies Cubic function redesign with varying Constants D, because its a lot easier to find Quadratic roots with changing Constants c than Cubic roots with changing Constants D.This post assumes math at the year 12 level.Before doing a couple of examples, lets do a brief recap on genetic Cubic architecture.Cubic Architecture RecapThe header graph shows reduced Cubic y=Ax+Cx+D and its genetic dimensions shown in black. It is rotationally symmetrical about its Inflection Point Ip(0, y)=Constant D; (Imaginary propellor shaft ?):):). It has y=Ip(y) intercepts as follows:Int A(x)= SqRt[-C/A] and Int B(x)= + SqRt[-C/A] with Midpoints:Midpoint (Int A : Ip(0, D)=Int A(x)-SqRt[-C/4A] and +SqRT[-C/4A] (not shown)And Turning Points Tp(x)=+-SqRt[-C/3A]Roots Rt 1, Rt 2 with Root Midpoint; Mid Point (Rt Read the full blog for free on Medium.Join thousands of data leaders on the AI newsletter. Join over 80,000 subscribers and keep up to date with the latest developments in AI. From research to projects and ideas. If you are building an AI startup, an AI-related product, or a service, we invite you to consider becoming asponsor. Published via Towards AITowards AI - Medium Share this post