Numerical Differentiation of Noisy, Nonsmooth Data

<table>The function <svg height="13.4875" id="M105" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.4875)">
<g transform="translate(72,-61.21)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑓</tspan>
</text>
</g>
</g>
</svg>, obtained from <svg height="13.45" id="M106" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 52.599998 13.45" width="52.599998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">|</tspan>
<tspan style="font-size: 12.50px; " x="2.5006001" y="0">𝑥</tspan>
<tspan style="font-size: 12.50px; " x="12.152916" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="23.493137" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="29.744637" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="33.22047" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="39.47197" y="0">|</tspan>
</text>
</g>
</g>
</svg> by adding Gaussian noise of standard deviation 0.05.</table>

International Scholarly Research Notices

Numerical Differentiation of Noisy, Nonsmooth Data

Figure 1