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feat: Starting theoretical description project C
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@ -57,4 +57,8 @@ https://tex.stackexchange.com/questions/294561/using-textbf-vs-mathbf-in-math-mo
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https://www.math-linux.com/latex-26/faq/latex-faq/article/how-to-get-dots-in-latex-ldots-cdots-vdots-and-ddots - Dots LaTeX
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https://www.overleaf.com/learn/latex/Tables - Tables LaTeX
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https://www.overleaf.com/learn/latex/Tables - Tables LaTeX
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https://en.wikibooks.org/wiki/LaTeX/Special_Characters - an arrow (circumflex) above letter in latex
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https://oeis.org/wiki/List_of_LaTeX_mathematical_symbols - For every symbol in LaTeX
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}
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\end{tabular}
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\end{center}
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We have to determine polynomial function $ y = f(x) $ that best fits this data.
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We have to determine polynomial function $ y = f(x) $ that best fits this data. \\
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We will use least-square approximation using system of normal equation with QR factorization.
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\section{Theoretical introduction}
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We have polynomial function:
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\[ y(x) = a_nx^n + a_{n-1}x^{n-1} + \dots + a_1x^1 + a_0 \]
|
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where n - degree of the polynomial we use to approximate function \\
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Given matrix $\mathbf{A} \in \mathbb{R}^{m \times n} \quad (m > n)$ and vector $\mathbf{y} \in \mathbb{R}^m$ \\
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We need to find vector \^{x} such that:
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\[ \forall x \in \mathbb{R}^n \quad|| \mathbf{y} - \mathbf{A} \hat{x} ||_2 \leq || \mathbf{y} - \mathbf{A}x ||_2 \]
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