September 2014
Intermediate to advanced
628 pages
24h 57m
English
Content preview from Numerical Linear Algebra with Applications
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Appendix C
Chebyshev Polynomials
Chebyshev polynomials have important uses in developing convergence results for algorithms; for instance, the analysis for the convergence of the conjugate gradient method in Chapter 21 can be done using these polynomials (see Ref. [1, pp. 312-316]). They also play a large role in convergence results for methods that compute eigenvalues of large sparse matrices (see Ref. [3, pp. 151-159]). There are additional applications to least-squares and interpolation. The book does not actually use Chebyshev polynomials in proofs, but the statement of certain theorems involve Chebyshev polynomials, and so we will give a brief overview of their definition and properties.
C.1 Definition
The definition begins with the form ...
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