- chap1.m Introduction
- chap2.m Chebyshev points and interpolants
- chap3.m Chebyshev polynomials and series
- chap4.m Interpolants, truncations, and aliasing
- chap5.m Barycentric interpolation formula
- chap6.m Weierstrass approximation theorem
- chap7.m Convergence for differentiable functions
- chap8.m Convergence for analytic functions
- chap9.m Gibbs phenomenon
- chap10.m Best approximation
- chap11.m Hermite integral formula
- chap12.m Potential theory and approximation
- chap13.m Equispaced points, Runge phenomenon
- chap14.m Discussion of higher-order polynomial interpolation
- chap15.m Lebesgue constants
- chap16.m Best and near-best
- chap17.m Orthogonal polynomials
- chap18.m Polynomial roots and colleague matrices
- chap19.m Clenshaw-Curtis and Gauss quadrature
- chap20.m Carathéodory-Fejér approximation
- chap21.m Spectral methods
- chap22.m Linear approximations: beyond polynomials
- chap23.m Nonlinear approximations: why rational functions?
- chap24.m Rational best approximation
- chap25.m Two famous problems
- chap26.m Rational interpolation and linearized least-squares
- chap27.m Padé approximation
- chap28.m Analytic continuation and convergence acceleration
- refs.m References
ERRATA
p 11: Exercise 2.2: in the final formula N should be n
p 22: Exercise 3.6: the exponent k-1 should be (k-1)/2
p 26: subscripts m should be n; -k(mod 2n) should be (-k)(mod 2n)
p 30: Exercise 4.4(d): length(f(np)) should be length(f(Mmax+1))
p 31: Exercise 4.6 should insert "(down to machine precision, in practice,
by Chebyshev interpolation)" before "and then"
p 47: Exercise 6.6(b): 2n should be 2n-1 (6 times)
p 51: 1.652783663415789e+04 should be 2.102783663403057e+04
p 54: Exercise 7.6(b): s=linspace(-1,1,10), p=chebfun(@(x) spline(s,exp(s),x));
p 57: just before the second displayed equation, (3.12) should be (3.13)
p 71: Exercise 9.8: sign(sin(x/2)) should be sign(x)
p 74: Bolzano-Weierstrass should be Heine-Borel
p 78: Exercise 10.1: after 'splitting','on' insert ,'minsamples',65
p 82: Cauchy stated a related formula but not exactly "the same result"
p 93: the product in (12.14) should run over j<k, not j≠k
p 119: the pointer to Exercise 10.5 should be to Exercise 10.6
p 127: the formulas need to be normalized by division by terms like (p_k,p_k)
pp 147, 151: Eqs. (19.10), (19.12) are incorrectly copied from
Trefethen (2008): (n-2ν-1)^{2ν+1} should be (2n+1-ν)^ν
p 160: "maps [-1,1]" should be "maps the unit circle"
p 166: Eq. (21.2) is incorrect (p. 166 and inside back cover)
p 215: the integral in (25.13) should have limits from -∞ to ∞
p 215: after (25.14), "even number" should be "odd number"
p 215: on the last line, type (n,n) should be type (n-1,n)
p 222: in (26.3), r(z) should be r(x)
p 229: the summation at the bottom needs a square root
p 256: Lottka should be Lotka
p 296: de la Vallée Poussin (1910) is missing an annotation
p 300: Borel should also list page 75
p 304: Richardson extrapolation should list pages 257-258
p 305: Weierstrass should not list page 75
CHANGES NEEDED FOR CHEBFUN VERSION 5
p 168:
[0 0 0 1 0] →
[0 0 0 1 0]'
OTHER NOTES
p 151: concerning Xiang and Bornemann [2012], Bornemann has
pointed out (personal communication, August 2013)
that just the right result
along these lines, derived from L
^{1} approximation, appeared years
ago as Theorem 2 in G. Freud, "Über einseitige Approximation
durch Polynome. I," Act. Sci. Math. Szeged 16 (1955), 12-28.