the functions x-xo x1 - x0 The linear Lagrange interpolating polynomial through (xo, yo) and (x₁, y₁) is P(x) = Lo(x) f(x) + L₁ (x) f(x₁) = Note that Lo(x) = which implies that X-X1 Xo-X1 and L₁(x) = X-XI Xo-X1 -f(x) + x-xo XI - Xo -f(x₁). Lo(x)= 1, Lo(x₁) = 0, L₁(x)=0, and L₁(x₁) = 1,

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
Section: Chapter Questions
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Make an actual code equivalent in MATLAB. Include the table showing the parameter values for each interpolation/iteration. Include graphs.

Define the functions
x-xo
x1 - x0
The linear Lagrange interpolating polynomial through (xo, yo) and (x₁, y₁) is
Note that
and
Lo(x) =
which implies that
X-X₁
Xo-X1
and L₁(x) =
P(x) = Lo(x) f(x) + L₁ (x) f(x₁); =
X-XI
XO-X1
-f(x0) +
x-xo
X1 Xo
Lo(x) = 1, Lo(x₁) = 0, L₁ (xo) = 0, and L₁ (x₁) = 1,
-f(x₁).
P(x)=1. f(x0) +0. f(x₁) = f(x) = yo
P(x₁) = 0. f(x) + 1 · ƒ(x₁) = f(x₁) = y₁.
So P is the unique polynomial of degree at most one that passes through (xo, yo) and
(X₁,Y₁).
Transcribed Image Text:Define the functions x-xo x1 - x0 The linear Lagrange interpolating polynomial through (xo, yo) and (x₁, y₁) is Note that and Lo(x) = which implies that X-X₁ Xo-X1 and L₁(x) = P(x) = Lo(x) f(x) + L₁ (x) f(x₁); = X-XI XO-X1 -f(x0) + x-xo X1 Xo Lo(x) = 1, Lo(x₁) = 0, L₁ (xo) = 0, and L₁ (x₁) = 1, -f(x₁). P(x)=1. f(x0) +0. f(x₁) = f(x) = yo P(x₁) = 0. f(x) + 1 · ƒ(x₁) = f(x₁) = y₁. So P is the unique polynomial of degree at most one that passes through (xo, yo) and (X₁,Y₁).
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