polyApprox | R Documentation |
Generate a polynomial approximation.
polyApprox(f, a, b, n, ...)
f |
function to be approximated. |
a , b |
end points of the interval. |
n |
degree of the polynomial. |
... |
further variables for function |
Uses the Chebyshev coefficients to derive polynomial coefficients.
List with four components:
p |
the approximating polynomial. |
f |
a function evaluating this polynomial. |
cheb.coeff |
the Chebyshev coefficients. |
estim.prec |
the estimated precision over the given interval. |
The Chebyshev approximation is optimal in the sense of the L^1
norm,
but not as a solution of the minimax problem; for this, an
application of the Remez algorithm is needed.
Carothers, N. L. (1998). A Short Course on Approximation Theory. Bowling Green State University.
chebApprox
, polyfit
## Example
# Polynomial approximation for sin
polyApprox(sin, -pi, pi, 9)
# $p
# [1] 2.197296e-06 0.000000e+00 -1.937495e-04 0.000000e+00 8.317144e-03
# [6] 0.000000e+00 -1.666468e-01 0.000000e+00 9.999961e-01 0.000000e+00
#
# $f
# function (x)
# polyval(p, x)
#
# $cheb.coeff
# [1] 0.06549943 0.00000000 -0.58518036 0.00000000 2.54520983 0.00000000
# [7] -5.16709776 0.00000000 3.14158037 0.00000000
#
# $estim.prec
# [1] 1.151207e-05
## Not run:
f <- polyApprox(sin, -pi, pi, 9)$f
x <- seq(-pi, pi, length.out = 100)
y <- sin(x) - f(x)
plot(x, y, type = "l", col = "blue")
grid()
## End(Not run)
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