-\chapterauthor{Gleb Beliakov and Shaowu Liu}{School of Information Technology, Deakin University, Burwood 3125, Australia}
+\chapterauthor{Gleb Beliakov and Shaowu Liu}{School of Information Technology, Deakin University, Burwood, Australia}
%\chapterauthor{Shaowu Liu}{School of Information Technology, Deakin University, Burwood 3125, Australia}
The rest of the chapter is organized as follows. Section \ref{ch11:splines} discusses monotone spline interpolation methods and presents two parallel algorithms. Section \ref{ch11:smoothing} deals with the smoothing problem. It presents the isotonic regression problem and discusses the Pool Adjacent Violators (PAV) and MLS algorithms. Combined with monotone spline interpolation, the parallel MLS method makes it possible to build a monotone spline approximation to noisy data entirely on GPU. Section \ref{ch11:conc} concludes.
-
+\clearpage
\section{Monotone splines} \label{ch11:splines}
\index{constrained splines} \index{monotonicity}
At the spline evaluation stage we need to compute $s(z_k)$ for a sequence of query values ${z_k}, k=1,\ldots,K$. For each $z_k$ we locate the interval $[t_i,t_{i+1}]$ containing $z_k$, using the bisection algorithm presented in Listing \ref{ch11:algeval}, and then apply the appropriate coefficients of the quadratic function. This is also done in parallel.
The bisection algorithm could be implemented using texture memory (to cache the array \texttt{z}), but this is not shown in Listing \ref{ch11:algeval}.
-%\pagebreak
-\lstinputlisting[label=ch11:algcoef,caption=Implementation of the kernel for calculating spline knots and coefficients; function fmax is used to avoid division by zero for data with coinciding abscissae.]{Chapters/chapter11/code1.cu}
+\pagebreak
+\lstinputlisting[label=ch11:algcoef,caption=implementation of the kernel for calculating spline knots and coefficients; function fmax is used to avoid division by zero for data with coinciding abscissae.]{Chapters/chapter11/code1.cu}
%% \begin{figure}[!hp]
