explicit_spline

The function computes the coefficients of the cubic polynomials as spline components of the clamped interpolating cubic spline of class <code>C^2</code> in its explicit form <code>S=B * gamma</code>.

We construct the explicit form of clamped cubic interpolating spline (both uniform - knots are equidistant and non-uniform - knots are arbitrary). Using this form, we propose a linear regression model suitable for real data smoothing.

Lubomir Antoni

ICSsmoothing

Data Smoothing by Interpolating Cubic Splines

Juraj Hudak

Csaba Torok

Viliam Kacala

explicit_spline function

<dl><dt>B</dt>
<dd>a <code>4</code>-element array of <code>(n+1)x(n+4)</code> matrices, whereas element in <code>i</code>-th row and <code>j</code>-th column of <code>l</code>-th matrix contains coefficient by <code>x^{l-1}</code> of cubic polynomial that is in <code>i</code>-th row and <code>j</code>-th column of matrix <code>B</code> from spline's explicit form <code>S=B.gamma</code>.</dd>
<dt>gamma</dt>
<dd>a vector of spline coefficients - function values and exterior-node derivatives that takes part in the explicit form \(S=B.\gamma\).</dd></dl>

Arguments

The function computes the coefficients of the cubic polynomials as spline components of the clamped interpolating cubic spline of class C^2 in its explicit form S=B * gamma. — explicit_spline

<dl>

<dt>B</dt>
<dd>a <code>4</code>-element array of <code>(n+1)x(n+4)</code> matrices, whereas element in <code>i</code>-th row and <code>j</code>-th column of <code>l</code>-th matrix contains coefficient by <code>x^{l-1}</code> of cubic polynomial that is in <code>i</code>-th row and <code>j</code>-th column of matrix <code>B</code> from spline's explicit form <code>S=B.gamma</code>.</dd>


<dt>gamma</dt>
<dd>a vector of spline coefficients - function values and exterior-node derivatives that takes part in the explicit form \(S=B.\gamma\).</dd>

</dl>

The function computes the coefficients of the cubic polynomials as spline components of the clamped interpolating cubic spline of class <code>C^2</code> in its explicit form <code>S=B * gamma</code>.

explicit_spline: The function computes the coefficients of the cubic polynomials as spline components of the clamped interpolating cubic spline of class `C^2` in its explicit form `S=B * gamma`.

Description

Usage

Value

Arguments

Examples