In Lecture 1, we solved the problem of finding a quadratic curve given three points on the curve. Let us generalize this. Suppose we are given m distinct points which lie on the curve of an unknown polynomial of degree n – 1. Set up optimization problems (solving the sub-questions for each case will help you in setting it up) and solve them to find the polynomial coefficients for the following cases: (In case the solution is not unique, devise a method to obtain the minimum Euclidean norm solution.)
In Lecture 1, we solved the problem of finding a quadratic curve given three points on the curve. Let us generalize this. Suppose we are given m distinct points which lie on the curve of an unknown polynomial of degree n – 1. Set up optimization problems (solving the sub-questions for each case will help you in setting it up) and solve them to find the polynomial coefficients for the following cases: (In case the solution is not unique, devise a method to obtain the minimum Euclidean norm solution.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.3: Quadratic Equations
Problem 82E
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