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Highlights from
Chebfun V4

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Chebfun V4

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30 Apr 2009 (Updated )

Numerical computation with functions instead of numbers.

Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

CHEBFUN GUIDE: INDEX

CHEBFUN GUIDE: INDEX

Contents

Chebfun commands and computer programs are given in capital letters. Entries are listed by section number.

A

ABS, 1.4, 2.1, 3.2, 9.2
accuracy, 1.1, 1.2, 1.5, 2.4, 4.2, 5.4, 7.7, 8.8
Airy functions, 3.1, 3.3
analytic functions, 2.2, 4.5, 5.2
ANGLE, 5.4
anonymous functions, 1.2, 7.3, 9.1, 10.4
approximation theory, chap. 4
Assheton, Phil, 1.1, 2.1
Automatic Differentiation, 2.4, 7.1, 7.8, 10.1, 10.3, 10.4

B

backslash, 6.2, chap. 7, 9.1, 10.4; see also nonlinear backslash
backward error analysis, 1.1, 2.4
barycentric interpolation, 1.2, 4.1, 4.5
Battles, Zachary, 1.1, 1.4, 3.1, 3.6, 4.5
Bernstein ellipse, 4.5
Bernstein, Sergey, 1.1, 4.1
Bessel functions, 1.2, 2.4
best or minimax approximation, 4.1, 4.6
Birkisson, Asgeir, 1.1, 7.1, 10.3
blowup, see infinite function values
'blowup', 1.5, 8.1, 8.9, 9.2, 9.3
Bornemann, Folkmar, 1.1, 7.2
boundary conditions, 7.4, 10.4
Boyd, John, 3.1, 3.6
breakpoints, 1.4, 3.2, 8.2
BVP4C/BVP/5C, 7.1, 7.8, chap. 10
BVPINIT, 10.2

C

Caratheodory-Fejer approximation, see CF
Carrier equation, 10.4
Cauchy integral, see contour integral
CEIL, 3.2
CF, 4.6, 4.8
changes of variables, see mappings
CHEBFUN, 1.2
CHEBFUNPREF, 2.5, chap. 8
'chebkind', 8.1
CHEBOPPREF, 8.1, 10.4
chebops, chap. 7, 8.7, chap. 10
CHEBPADE, 4.8
CHEBPOLY, 1.3, 2.6, 4.2, 6.4
CHEBPTS, 2.6
Chebyshev approximation, see best or minimax approximation
Chebyshev coefficients, 4.1, 4.2, 7.7, 8.6, 9.3
Chebyshev interpolant, 4.1, 4.2
Chebyshev-Pade approximation, 4.8
Chebyshev, Pafnuty Lvovich, 4.1, 5.5
Chebyshev points, 1.1, 1.2, 4.2, 4.7
Chebyshev polynomials, 1.1, 4.1, 6.4, 9.3
Chebyshev series, 4.1, 4.2, 4.8
Clenshaw-Curtis quadrature, 1.2, 2.1, 2.6
colleague matrix, 3.1
complex roots, 3.6, 5.4
complex variables, chap. 5
COND, 6.4
conformal map, 5.2
contour integral, 5.3, 5.4
COTEDA, 2.1
CUMSUM, 2.3, 2.4, 7.3, 9.1

D

DBLQUAD, 2.5
DEFINE, 1.3
delta functions, 2.4
DIAG, 7.3
DIFF, 2.4, 3.3, 7.3, 10.3
differential equations, see ODEs and PDEs
diffusion, 7.6
diverging functions, 1.5
DIFF, 2.4, 3.3, 7.3
'dirichlet', 7.4
discontinuities, 3.2
'domain', 8.1, 8.2
DOMAIN, 1.3, 7.4
Driscoll, Toby, 1.1, chap. 7, 10.2, 10.3

E

edge detection, 1.4, 8.3
eigenvalues problems, 7.5
EIGS, 7.5
.ends, 9.1
'eps', 2.5, 8.1, 8.1, 8.8
equispaced points, 4.7
error function, 2.1, 2.3, 9.1
EXPM, 7.6
'exps', 9.2
exponential of an operator, 7.6
'extrapolate', 8.1
extrema, 3.3, 3.4
EYE, 7.3

F

'factory', 1.4, 8.1
factory values, see 'factory'
FFT, 1.1, 2.1, 4.1
File Exchange, 1.1
FILL, 5.2
FLOOR, 3.2
fourfun, 5.3
Frechet derivative, see Jacobian
Frobenius norm, 6.4
.funs, 1.4, 9.1
funs, 1.4, 2.1

G

gamma function, 9.1
Gauss quadrature, 2.6
Gauss-Jacobi quadrature, 2.6, 9.2
Gibbs phenomenon, 4.3
Glaser-Liu-Rokhlin algorithm, 2.6
Golub-Welsch algorithm, 2.6
Gonnet, Pedro, 1.1, 2.1, 4.8
GREETINGCARD, 5.5
GUIDEDEFAULTS, 1.7

H

Hale, Nick, 1.1, 1.5, 2.6, 9.2
Higham, Nick, 1.2, 4.5
Hilbert-Schmidt norm, see Frobenius norm

I

.imps, 1.4
infinite function values, 1.5, 2.1, 9.2
infinite intervals, 1.5, 2.1, 9.1
inner product, 1.6, 6.1
integral equations, 7.4
integrals, 1.2, 1.5, chap. 2, 9.1
integrals in 2D, 2.5
interpolation, 1.2
INTERP1, 4.7, 4.8
'interval', 4.3, 9.1

J

JACPOLY, 2.6
JACPTS, 2.6, 9.2, 9.3
.jacobian, 1.4, 9.1
Jacobian, 7.8, 10.3, 10.4

K

L

least-squares, 6.2
Lebesgue function, see LEBESGUE
LEBESGUE, 4.7
Legendre polynomials, see LEGPOLY
LEGPOLY, 2.6, 6.3, 6.4
LEGPTS, 2.6
LENGTH, 1.2, 1.4
LINSOLVE, 10.4
Lorenz equations, 10.1

M

MAP, 9.3
mappings, 9.1, 9.3
Mathematica, 2.1
Mathieu equation, 7.5
Maxwell's equations, 7.9
MEAN, 2.2
meromorphic function, 5.2
METHODS, 1.3
MAX, 3.2, 3.4
'maxdegree', 8.1, 8.5
MIN, 3.2, 3.4
MINANDMAX, 3.4, 10.1
'minsamples', 8.1, 8.6
MLDIVIDE, 6.2, 10.3
Moebius transformation, 5.2
monomial basis, 4.2

N

NaN, 9.2
'neumann', 7.4
Newton iteration, 2.4, 7.1, 7.8, 9.4, chap. 10
.nfuns, 1.4, 9.1
nonlinear backslash, 7.1, 7.8, 10.1, 10.4
nonlinera chebops, chap. 10
NORM, 2.2, 3.5, 6.4, 6.5
NULL, 6.6

O

ODE45/ODE15S/ODE113, 10.1, 10.2
ODEs, chap. 7, chap. 10
ODESET, 10.1
Olver, Sheehan, 1.1
Orr-Sommerfeld equation, 7.5
ORTH, 6.6
orthogonal polynomials, 6.3, 9.3
overloading, 1.1, 1.3

P

Pachon, Ricardo, 1.1, 1.4, 4.6, 4.8
Pade approximation, 4.8
path, 1.7
PDE15S, 7.1, 10.1
PDEs, 7.1, 7.6
periodic functions, 5.3, 7.4, 7.5
piecewise smooth chebfuns, 1.4, 2.1, 5.1
PINV, 6.6
Platte, Rodrigo, 1.1, 1.4, 1.5, 9.1, 9.2, 10.2
PLOT, 1.2, 9.1
'plotting', 10.4
PLUS, 1.3
poles, 4.8, 5.4, 9.2
POLY, 4.2
POLYFIT, 4.8
polynomial interpolation, 1.1, 1.2
POWER, 1.3
PUBLISH, 1.7

Q

QR, 6.3
QR factorization, 6.3
QUAD, QUADL, QUADGK, 2.1
QUADPACK, 2.1
quadrature, see integration
quasimatrices, 1.6, 5.1, chap. 6

R

RATINTERP, 4.8
RDIVIDE, 1.3
REMEZ, 1.3, 4.6, 4.8
Remez algorithm, 4.6
'resampling', 8.1, 8.7
residue, 5.3
Richardson, Mark, 1.1, 1.5, 9.2
ROOTS, 1.1, 1.2, 3.1, 9.1
ROUND, 3.2
rounding errors, 1.1, 4.5
row vs. column chebfuns, 1.6, 6.1
Runge function, 1.2, 4.4
Runge phenomenon, 4.4, 4.7

S

Salzer, Herbert, 1.2, 4.1
Scheuring, Simon, 1.1
.scl, 1.4, 9.1
SCRIBBLE, 5.5, 7.6
SIGN, 3.2, 4.3, 8.5
sinc function, 9.1
'singmap', 9.3
singularities, 2.6, 8.3, 8.5, 9.2, 9.3
SIZE, 6.1
smoothness, 4.1, 4.4
SOLVEBVP, 7.1, 7.8, 10.4
spectral accuracy, 4.4
spectral methods, 4.1, chap. 7, 8.7, chap. 10
spline, 6.2
'splitdegree', 8.1, 8.4
'splitting', 1.4, 4.1, 8.1, 8.3
SPY, 6.1, 6.3, 6.6
square root, 2.1, 8.3, 9.2
stability, 1.2
STD, 1.4, 2.2
stiffness, 10.1, 10.4
STRUCT, 1.4
SUBSREF, 1.3
SUM, 1.2, 2.1
SVD, 6.4
symbolic computing, 1.1
systems of equations, 7.9

T

Taylor coefficients, 4.2, 5.3, 5.4
.trans, 1.4, 9.1
transpose, 1.6

U

UNWRAP, 5.4

V

van der Pol equation, 10.1, 10.4
Van Deun, Joris, 1.1, 4.6, 4.8
VAR, 2.2
'vectorize', 2.5

Z

zeros, 5.4, also see ROOTS

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