polynomial_solve_with_smoothing.tex File Reference

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Variables
	documentclass
we have to be quite careful how things are indexed For	example
we have to be quite careful how things are indexed For consider the generalised quadratic polynomial in two dimensions	begin
we have to be quite careful how things are indexed For consider the generalised quadratic polynomial in two dimensions this is termed	emph
we have to be quite careful how things are indexed For consider the generalised quadratic polynomial in two dimensions this is termed we index the $i in the product of	$x_i

Variable Documentation

we have to be quite careful how things are indexed For consider the generalised quadratic polynomial in two dimensions this is termed we index the $i in the product of $x_i

Definition at line 32 of file polynomial_solve_with_smoothing.tex.

we have to be quite careful how things are indexed For consider the generalised quadratic polynomial in two dimensions this is termed we index the $i in the product of so for example the quadratic equation above becomes begin

Initial value:

{equation}
\label{eq:quadratic}
y = a_{00} + a_{10} x_0 + a_{01} x_1 + a_{11} x_0 x_1 + a_{20} x_0^2 + a_{02} x_1^2
\end{equation}

The polynomial coefficients $a_{jk}$ have been indexed by the power on the
corresponding products of $x_i$. Explicitly

Definition at line 19 of file polynomial_solve_with_smoothing.tex.

documentclass

Initial value:

{article}
\usepackage{graphicx}

\begin{document}

\section{Arbitrary Order, Arbitrary Dimensional Polynomial Solve With Smoothing}

\emph{Chris Rogers, STFC Rutherford Appleton Laboratory, 2015}

Below I outline the mathematical foundation for higher order polynomial solving.

\subsection{Generalised Indexing and Notation}

The polynomial solve is a quite straightforward consequence of a simultaneous
equation solve. The only really tricky thing is one of notation. For a 
polynomial in higher dimensional space

Definition at line 1 of file polynomial_solve_with_smoothing.tex.

we have to be quite careful how things are indexed For consider the generalised quadratic polynomial in two dimensions this is termed emph

Initial value:

{index by power}. Occasionally we also use the concept of \emph{index by 
vector}. In this indexing scheme

Definition at line 32 of file polynomial_solve_with_smoothing.tex.

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Definition at line 1 of file polynomial_solve_with_smoothing.tex.