Farm X-1 Lux(x) 1 This polynomial is given by The interpolating polynomial is easily described once the form of Lnk is known. This polynomial, called the nth Lagrange interpolating polynomial, is defined in the following theorem. Ln(x) = If x0, x₁,...,x are n + 1 distinct numbers and f is a function whose values are given at these numbers, then a unique polynomial P(x) of degree at most n exists with f(x) = P(x), for each k = 0, 1,..., n. where, for each k = 0, 1,..., n, = xk Xx+1 R II i=0 izk 11 P(x) = f(x)L₂,0 (x) + ··· + ƒ (X₂)Ln,n(X) = Σƒ (Xk) Ln,k (X), k=0 (x-xo)(x-x₁)··· (X − Xk-1) (X — Xk+1) ・・・ (X−X₂) (Ik – X0)(Xk − Xi)…( − Xk−1)(x − Xk+1) … ( −x) (x-x₂) (X – Xì) - x (3.1) (3.2)

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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
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Make an actual code equivalent in MATLAB. Include the table showing the parameter values for each interpolation/iteration. Include graphs.

L₁(x) 4
This polynomial is given by
x₁
Lnk (x) =
The interpolating polynomial is easily described once the form of Lnk is known. This
polynomial, called the nth Lagrange interpolating polynomial, is defined in the following
theorem.
where, for each k = 0, 1,...,n,
=
If x0, x₁,...,x, are n + 1 distinct numbers and f is a function whose values are given at
these numbers, then a unique polynomial P(x) of degree at most n exists with
f(x) = P(x), for each k = 0, 1,...,n.
X-1
n
II
i=0
izk
Xk
Xx+1
(x-x₂)
(NG – xì)
X-1
P(x) = f(xo)Lo(x) + - · ·· + ƒ (Xn)Ln,n(X) = Σf(xx) Ln,k (x),
k=0
(x-xo)(x-x₁)··· (X − Xk−1) (X — Xk+1) (X−Xn)
(*k – X0)(Xk − Xi)… ( − −1)( − Xk+t) … ( −x)
(3.1)
(3.2)
Transcribed Image Text:L₁(x) 4 This polynomial is given by x₁ Lnk (x) = The interpolating polynomial is easily described once the form of Lnk is known. This polynomial, called the nth Lagrange interpolating polynomial, is defined in the following theorem. where, for each k = 0, 1,...,n, = If x0, x₁,...,x, are n + 1 distinct numbers and f is a function whose values are given at these numbers, then a unique polynomial P(x) of degree at most n exists with f(x) = P(x), for each k = 0, 1,...,n. X-1 n II i=0 izk Xk Xx+1 (x-x₂) (NG – xì) X-1 P(x) = f(xo)Lo(x) + - · ·· + ƒ (Xn)Ln,n(X) = Σf(xx) Ln,k (x), k=0 (x-xo)(x-x₁)··· (X − Xk−1) (X — Xk+1) (X−Xn) (*k – X0)(Xk − Xi)… ( − −1)( − Xk+t) … ( −x) (3.1) (3.2)
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