Merge pull request #142 from numlinalg/v0.2-man-linear-system

Manual: Linear Systems

Author: vp314

docs/make.jl

@@ -18,6 +18,8 @@ makedocs(
         "Manual" => [
             "Introduction" => "manual/introduction.md", 
             "Compression" => "manual/compression.md",
+            "Low-Rank Approximation" => "manual/low_rank_approximators.md",
+            "Linear Systems" => "manual/linear_systems.md"
         ],
         "Tutorials" => [
             "tutorials/tutorials_overview.md",

docs/src/api/solvers.md

@@ -1,4 +1,4 @@
-# Solvers  
+# Solvers API 
 ```@contents
 Pages = ["solvers.md"]
 ```

docs/src/manual/images/kaczmarz.svg

@@ -0,0 +1,42 @@
+\documentclass[tikz,convert={outfile=kaczmarz.svg}]{standalone}
+\usepackage{graphicx} % Required for inserting images
+\usepackage{tikz}
+\title{projection drawings}
+\author{Nathaniel Pritchard}
+\date{October 2025}
+\definecolor{myred}{RGB}{203, 144, 77}
+\definecolor{mygreen}{RGB}{195, 233, 145}
+\definecolor{mynavy}{RGB}{81, 163, 163}
+\definecolor{lager}{RGB}{223, 204, 116}
+\definecolor{regal}{RGB}{117, 72, 94}
+\begin{document}
+       \begin{tikzpicture}
+        \draw[color=mynavy] (0,0) -- (0,4);
+        \node[color = mynavy] at (-.3,0) {$\mathcal{H}_1$};
+        \draw[color=lager] (-2,2) -- (2,2);
+        \node[color = lager] at (2.3,2) {$\mathcal{H}_4$};
+        \draw[color=mygreen] (-2,0) -- (2,4);
+        \node[color = mygreen] at (2.3,4) {$\mathcal{H}_3$};
+        \draw[color=regal] (-2,4) -- (2,0);
+        \node[color = regal] at (2.3,0) {$\mathcal{H}_2$};
+        \filldraw[black] (0,2) circle (2pt);
+        {\filldraw[black] (1.5,2.5) circle (2pt);}
+        {\draw[very thick] (1.5,2.5) -- (1.5,2);}
+        {\draw[very thick] (1.5,2) -- (.75,1.25);}
+        {\filldraw[red] (1.5,2) circle (2pt);}
+         {\draw[very thick] (.75,1.25) -- (0,1.25);}
+         {\filldraw[red] (.75,1.25) circle (2pt);}
+          {\draw[very thick] (0,1.25) -- (-.375, 1.625);}
+          {\filldraw[red] (0,1.25) circle (2pt);}
+          {\draw[very thick] (-.375, 1.625) -- (-.375,2);}
+          {\filldraw[red] (-.375, 1.625) circle (2pt);}
+          {\draw[very thick] (-.375,2) -- (-.1875, 2.1875);}
+          {\filldraw[red] (-.375,2) circle (2pt);}
+          {\draw[very thick] (-.1875, 2.1875) -- (0, 2.1875);}
+          {\filldraw[red] (-.1875, 2.1875) circle (2pt);}
+          {\draw[very thick] (0, 2.1875) -- (0.09374, 2.09374);}
+          {\filldraw[red] (0, 2.1875) circle (2pt);}
+          {\draw[very thick] (0.09374, 2.09374) -- (0, 2.09374);}
+          {\filldraw[red](0.09374, 2.09374) circle (2pt);}
+    \end{tikzpicture}
+\end{document}