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Consider the polynomial of order 4 shown below. f(x) = c +c₁x + c₂x² + C3x³ + C4x4 The polynomial satisfies the following conditions: f(-3) = 5.0 f(-1.5) = 3.0 f(-0) = 0.0 ƒ(2.5) = 6 ƒ(6) = 8.5 a) In trying to interpolate the above points to fit the 4th order polynomial, please show the matrix vector equations in the text cell below to solve. (NOTE: You don't need to solve the equations manually. Just showing the matrix vector equations, and word explanations in writing is fine. Fill it either in latex equations or upload a written answer) b) Find the coefficients for interpolating the above conditions into a 4th degree polynomial using python. Define a function for the interpolating polynomial. (NOTE: Setup the matrices as numpy arrays, solve them using python standard functions.)

Consider the polynomial of order 4 shown below. f(x) = c +c₁x + c₂x² + C3x³ + C4x4 The polynomial satisfies the following conditions: f(-3) = 5.0 f(-1.5) = 3.0 f(-0) = 0.0 ƒ(2.5) = 6 ƒ(6) = 8.5 a) In trying to interpolate the above points to fit the 4th order polynomial, please show the matrix vector equations in the text cell below to solve. (NOTE: You don't need to solve the equations manually. Just showing the matrix vector equations, and word explanations in writing is fine. Fill it either in latex equations or upload a written answer) b) Find the coefficients for interpolating the above conditions into a 4th degree polynomial using python. Define a function for the interpolating polynomial. (NOTE: Setup the matrices as numpy arrays, solve them using python standard functions.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.3: Change Of Basis
Problem 17EQ
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Ignore the python part, for part b , just define a function for interpolating polynomial

Consider the polynomial of order 4 shown below. f(x) = co+c₁x + c₂x² + c3x³ + C4x4 The polynomial satisfies the following conditions: f(-3) = 5.0 f(-1.5) = 3.0 f(0) = 0.0 ƒ(2.5) = 6 f(6) = 8.5 a) In trying to interpolate the above points to fit the 4th order polynomial, please show the matrix vector equations in the text cell below to solve. (NOTE: You don't need to solve the equations manually. Just showing the matrix vector equations, and word explanations in writing is fine. Fill it either in latex equations or upload a written answer) b) Find the coefficients for interpolating the above conditions into a 4th degree polynomial using python. Define a function for the interpolating polynomial. (NOTE: Setup the matrices as numpy arrays, solve them using python standard functions.)
Transcribed Image Text:Consider the polynomial of order 4 shown below. f(x) = co+c₁x + c₂x² + c3x³ + C4x4 The polynomial satisfies the following conditions: f(-3) = 5.0 f(-1.5) = 3.0 f(0) = 0.0 ƒ(2.5) = 6 f(6) = 8.5 a) In trying to interpolate the above points to fit the 4th order polynomial, please show the matrix vector equations in the text cell below to solve. (NOTE: You don't need to solve the equations manually. Just showing the matrix vector equations, and word explanations in writing is fine. Fill it either in latex equations or upload a written answer) b) Find the coefficients for interpolating the above conditions into a 4th degree polynomial using python. Define a function for the interpolating polynomial. (NOTE: Setup the matrices as numpy arrays, solve them using python standard functions.)
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