How do I expand the Hermite Cubic Spline basis to the nth order?
$begingroup$
A useful basis for cubic polynomials are those used for Hermite interpolation:
$$h_{00}(t) = 2t^3-3t^2+1$$
$$h_{10}(t) = t^3-2t^2+t$$
$$h_{01}(t) = -2t^3+3t^2$$
$$h_{11}(t) = t^3-t^2$$
It is also possible to construct similar functions for interpolating with quintic polynomials. Is there a way to generate the polynomials for interpolating with $2k+1$th order polynomials, for $k in mathbb{Z}$
polynomials interpolation hermite-polynomials
$endgroup$
add a comment |
$begingroup$
A useful basis for cubic polynomials are those used for Hermite interpolation:
$$h_{00}(t) = 2t^3-3t^2+1$$
$$h_{10}(t) = t^3-2t^2+t$$
$$h_{01}(t) = -2t^3+3t^2$$
$$h_{11}(t) = t^3-t^2$$
It is also possible to construct similar functions for interpolating with quintic polynomials. Is there a way to generate the polynomials for interpolating with $2k+1$th order polynomials, for $k in mathbb{Z}$
polynomials interpolation hermite-polynomials
$endgroup$
add a comment |
$begingroup$
A useful basis for cubic polynomials are those used for Hermite interpolation:
$$h_{00}(t) = 2t^3-3t^2+1$$
$$h_{10}(t) = t^3-2t^2+t$$
$$h_{01}(t) = -2t^3+3t^2$$
$$h_{11}(t) = t^3-t^2$$
It is also possible to construct similar functions for interpolating with quintic polynomials. Is there a way to generate the polynomials for interpolating with $2k+1$th order polynomials, for $k in mathbb{Z}$
polynomials interpolation hermite-polynomials
$endgroup$
A useful basis for cubic polynomials are those used for Hermite interpolation:
$$h_{00}(t) = 2t^3-3t^2+1$$
$$h_{10}(t) = t^3-2t^2+t$$
$$h_{01}(t) = -2t^3+3t^2$$
$$h_{11}(t) = t^3-t^2$$
It is also possible to construct similar functions for interpolating with quintic polynomials. Is there a way to generate the polynomials for interpolating with $2k+1$th order polynomials, for $k in mathbb{Z}$
polynomials interpolation hermite-polynomials
polynomials interpolation hermite-polynomials
asked Jan 8 at 20:39
Fred FreyFred Frey
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