Carlo Gasbarri: Liouville’s inequality for transcendental points on projective varieties
Abstract: Liouville inequality is a lower bound of the norm of an integral section of a line bundle on an algebraic point of a variety. It is an important tool in may proofs in diophantine geometry and in transcendence. On transcendental points an inequality as good as Liouville inequality
From playlist Algebraic and Complex Geometry
Why do we have to flip the sign when we divide or multiply by negative one - Cool Math
👉 Learn about solving an inequality and graphing it's solution. An inequality is a relation where the expression in the left hand side is not equal to the expression in the right hand side of the inequality sign. A linear inequality is an inequality whose highest power in the variable(s) i
From playlist Solve and Graph Inequalities | Learn About
Steffensen's Method with Aitken's Δ²
Discussion of Steffensen's Method and Aitken's Delta-Squared Method with their relation to Fixed Point Iteration including examples, convergence acceleration, order, and code. GitHub: https://github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:08 Aitken's Δ² Method History 0:23 Deriv
From playlist Root Finding
Generalized Aitken-Steffensen Method
Generalized Aitken's delta-squared method and Generalized Steffensen's Method applying Fixed Point Iteration to Systems of Nonlinear Equations. Video goes step-by-step to derive Generalized Aitken-Steffensen and discusses induced and accelerated convergence behavior as well as quadratic or
From playlist Solving Systems of Nonlinear Equations
Steffensen's Method for Systems of Nonlinear Equations
Generalized Steffensen's Method for Simultaneous Nonlinear Systems originally credited to J. F. Traub. Video shows how to solve nonlinear systems by approximating the Jacobian. Example code on GitHub https://www.github.com/osveliz/numerical-veliz Chapters 0:00 Prerequisites 0:20 Intro 0:
From playlist Solving Systems of Nonlinear Equations
Approximating the Jacobian: Finite Difference Method for Systems of Nonlinear Equations
Generalized Finite Difference Method for Simultaneous Nonlinear Systems by approximating the Jacobian using the limit of partial derivatives with the forward finite difference. Example code on GitHub https://www.github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:13 Prerequisites 0:3
From playlist Solving Systems of Nonlinear Equations
Algebra - Ch. 31: Linear Inequality in 2 Variables (2 of 14) Differences
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn the difference between “greater-than or equalto” and “greater-than”, and “less-than or equal to” and “less-than” graphi
From playlist ALGEBRA CH 31 LINEAR INEQUALITIES IN 2 VARIABLES
Wegstein Method for finding roots, accelerating fixed point iteration, and inducing convergence in fixed point iteration. Explained examples and discussion of order as well as how to compute q. Example code: https://github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:22 Wegstein's Me
From playlist Root Finding
Solving and graphing a linear inequality
👉 Learn how to solve multi-step linear inequalities having no parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-ste
From playlist Solve and Graph Inequalities | Multi-Step Without Parenthesis
Fixed Point Iteration method for finding roots of functions. Frequently Asked Questions: Where did 1.618 come from? If you keep iterating the example will eventually converge on 1.61803398875... which is (1+sqrt(5))/2. Why not use x = x^2 -1? Generally you try to reduce the degree of the
From playlist Root Finding
Solving a linear inequality with fractions
👉 Learn how to solve multi-step linear inequalities having no parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-ste
From playlist Solve and Graph Inequalities | Multi-Step Without Parenthesis
Converge order and error reduction can be confusing but this video breaks it down and provides examples showing how order relates to speed and runtime. It also explains how order of convergence relates to Big O. Watching the other videos on this channel can be helpful but is not necessary.
From playlist Root Finding
Fixed Point Iteration Method followup video answering your frequently asked questions like "How do you pick a starting point?" and "How do you use the convergence test without the root?" Example code can be found at https://github.com/osveliz/numerical-veliz specifically in the programs fo
From playlist Root Finding
How to solve and graph one variable inequalities
👉 Learn about solving an inequality and graphing it's solution. An inequality is a relation where the expression in the left hand side is not equal to the expression in the right hand side of the inequality sign. A linear inequality is an inequality whose highest power in the variable(s) i
From playlist Solve and Graph Inequalities | Learn About
Fixed Point Iteration System of Equations with Banach
Fixed Point Iteration Method to solve Systems of Nonlinear Equations with discussion of Banach Fixed Point Theorem, finding the Jacobian, convergence, and order. Example code on GitHub: http://github.com/osveliz/numerical-veliz Chapters: 00:00 Intro 00:25 Systems of Equations 00:33 Solvin
From playlist Solving Systems of Nonlinear Equations
Solving and graphing a one variable inequality with variable on both sides
👉 Learn how to solve multi-step linear inequalities having no parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-ste
From playlist Solve and Graph Inequalities | Multi-Step Without Parenthesis
Solving a multi-step inequality with variables on both sides
👉 Learn how to solve multi-step linear inequalities having no parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-ste
From playlist Solve and Graph Inequalities | Multi-Step Without Parenthesis
Solving and graphing an inequality
👉 Learn how to solve multi-step linear inequalities having parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-step l
From playlist Solve and Graph Inequalities | Multi-Step With Parenthesis
Generalized False Position & Alternative Secant Methods
False Position Method for Nonlinear Systems (aka Generalized Regula Falsi) along with two Alternative Secant Methods. Includes discussion of history and primary sources along with numeric examples and visualizations. Example code hosted on GitHub https://github.com/osveliz/numerical-veliz
From playlist Solving Systems of Nonlinear Equations