INDEX

adaptive, 18

alternating algorithm, 75

alternation, 4-5, 71-72

analytic

continuation, 44

function, 17, 22, 35, 89

approximation,

adaptive, 17-18

best, 2, 67

L2, 22, 24

complex, 21

good,10

linear, 55

near-best, 22

nonlinear, 16, 72

polynomial, see polynomial

rational, see rational

attenuation factors, 88

Bernstein, 10, 12, 16, 34, 56, 111, 115

Bezier representation

of a pp function, 103

Bezout's theorem, 92

bivariate, 76-78

Blaschke product, 31

blending methods, 76

box spline, 100, 116-125

B-spline, 87, 92, 100, 103

calculation of b.a., 8

Caratheodory-Fejer Theorem, 32

capacity, 29

CF approximation, 32

characterization

of b.a., 5, 30

Chebyshev

expansion or series, 28

polynomials, 9, 11, 28, 31, 57

space, 6

system, 6, 85-86, 89

Chebyshev's Theorem, 4

Christoffel numbers, 42

circularity (of the error), 31-32

computer-aided design, 116

continued fraction, 38

control polygon, 123

convexity

strict, 3

convolution, 13

degree of approximation, 12, 23, 34,

43-44, 121

differential correction (algorithm), 72

Diliberto-Straus (algorithm), 74

dist, 2, 67-68

divided difference, 82

duality, 57, 68, 92

eigenvalues, 32, 59, 96-97

electrostatics, 29

entire (functions), 23, 40

equi-oscillation (criterion), 71-72

exchange method, 70

existence, 2, 43

exponentials, 6

Faber

polynomials, 26

series, 26-28

Favard, 12

Fejer, 32

Fekete points, 29

finite element, 117

Fourier

series, 8, 88

transform, 119

discrete, 88

fast, 85

129