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L₁(x) in the Lagrange form of the polynomial interpolant are basis functions for the space of polynomials of degree n. In this problem we'll establish a more explicit connection. (a) Suppose we're given the data {(1, 1), (2,3), (3, 1)}. In general, the polymomial interpolant for this data is given by (1) p(x) = a₁ + a₁x + a₂x². (2) Using the data (1), write down a linear system of equations in matrix form Ma = f for the coefficients a¿, i = 0, 1, 2 in (2). What is the solution a?

L₁(x) in the Lagrange form of the polynomial interpolant are basis functions for the space of polynomials of degree n. In this problem we'll establish a more explicit connection. (a) Suppose we're given the data {(1, 1), (2,3), (3, 1)}. In general, the polymomial interpolant for this data is given by (1) p(x) = a₁ + a₁x + a₂x². (2) Using the data (1), write down a linear system of equations in matrix form Ma = f for the coefficients a¿, i = 0, 1, 2 in (2). What is the solution a?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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L₁(x) in the Lagrange form of the polynomial interpolant are basis functions for the space of polynomials of degree n. In this problem we'll establish a more explicit connection. (a) Suppose we're given the data {(1, 1), (2, 3), (3, 1)) In general, the polymomial interpolant for this data is given by (1) p(x) = a₁ + a₁x + a₂x². (2) Using the data (1), write down a linear system of equations in matrix form Ma = f for the coefficients a¿, i = 0, 1, 2 in (2). What is the solution a?
Transcribed Image Text:L₁(x) in the Lagrange form of the polynomial interpolant are basis functions for the space of polynomials of degree n. In this problem we'll establish a more explicit connection. (a) Suppose we're given the data {(1, 1), (2, 3), (3, 1)) In general, the polymomial interpolant for this data is given by (1) p(x) = a₁ + a₁x + a₂x². (2) Using the data (1), write down a linear system of equations in matrix form Ma = f for the coefficients a¿, i = 0, 1, 2 in (2). What is the solution a?
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