Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let 2₁, 22, ..., 2 be distinct complex numbers. We define the ith Lagrange polynomial to be and note immediately that P:(2) = II 2-2; 2₁-2; Pi(2j) = díj, where §¡¡ is the Kronecker delta. We now observe that if P(2) is any polynomial of Hegree less than or equal to (k − 1), we have the following representation for P(2): P(2) = Σ P{(^)P(2₂), i=1

Let 2₁, 22, ..., 2 be distinct complex numbers. We define the ith Lagrange polynomial to be and note immediately that P:(2) = II 2-2; 2₁-2; Pi(2j) = díj, where §¡¡ is the Kronecker delta. We now observe that if P(2) is any polynomial of Hegree less than or equal to (k − 1), we have the following representation for P(2): P(2) = Σ P{(^)P(2₂), i=1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 4E
See similar textbooks
icon
Related questions
Question

Request explain the highlighted portion

Let 2₁, 22, ..., 2 be distinct complex numbers. We define the ith Lagrange polynomial to be and note immediately that Pi(2) = II j=12₁-2₂ Pi(2j) = díj, where 8, is the Kronecker delta. We now observe that if P(2) is any polynomial of degree less than or equal to (k − 1), we have the following representation for P(2): P(2) = Σ P:{(2)P(2), i=1
Transcribed Image Text:Let 2₁, 22, ..., 2 be distinct complex numbers. We define the ith Lagrange polynomial to be and note immediately that Pi(2) = II j=12₁-2₂ Pi(2j) = díj, where 8, is the Kronecker delta. We now observe that if P(2) is any polynomial of degree less than or equal to (k − 1), we have the following representation for P(2): P(2) = Σ P:{(2)P(2), i=1
Expert Solution
steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS