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CHEBYSHEV POLYNOMIALS Chebyshev polynomials are used in many parts of nu-
 

Summary: CHEBYSHEV POLYNOMIALS
Chebyshev polynomials are used in many parts of nu-
merical analysis, and more generally, in applications
of mathematics. For an integer n 0, define the
function
Tn(x) = cos

n cos-1 x

, -1 x 1 (1)
This may not appear to be a polynomial, but we will
show it is a polynomial of degree n. To simplify the
manipulation of (1), we introduce
= cos-1(x) or x = cos(), 0 (2)
Then
Tn(x) = cos(n) (3)
Example. n = 0
T0(x) = cos(0 ) = 1
n = 1
T1(x) = cos() = x

  

Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa

 

Collections: Computer Technologies and Information Sciences