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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,