Fix smaller formating issues in docu

docs/src/literate/examples/compressed_sensing.jl

@@ -46,7 +46,7 @@ fig
 # To recover the image from the measurement vector, we solve the TV-regularized least squares problem:
 # ```math
 # \begin{equation}
-#   \underset{\mathbf{x}}{argmin} \frac{1}{2}\vert\vert \mathbf{A}\mathbf{x}-\mathbf{b} \vert\vert_2^2 + \vert\vert\mathbf{x}\vert\vert_{\lambda\text{TV}} .
+#   \underset{\mathbf{x}}{argmin} \frac{1}{2}\vert\vert \mathbf{A}\mathbf{x}-\mathbf{b} \vert\vert_2^2 + \lambda\vert\vert\mathbf{x}\vert\vert_{\text{TV}} .
 # \end{equation}
 # ```
 

docs/src/literate/examples/computed_tomography.jl

@@ -13,7 +13,7 @@ N = 256
 image = shepp_logan(N, SheppLoganToft())
 size(image)
 
-# This produces a 64x64 image of a Shepp-Logan phantom. 
+# This produces a 256x256 image of a Shepp-Logan phantom. 
 
 using RadonKA, LinearOperatorCollection
 angles = collect(range(0, π, 256))
@@ -43,7 +43,7 @@ fig
 # To recover the image from the measurement vector, we solve the $l^2_2$-regularized least squares problem
 # ```math
 # \begin{equation}
-#   \underset{\mathbf{x}}{argmin} \frac{1}{2}\vert\vert \mathbf{A}\mathbf{x}-\mathbf{b} \vert\vert_2^2 + \vert\vert\mathbf{x}\vert\vert^2_2 .
+#   \underset{\mathbf{x}}{argmin} \frac{1}{2}\vert\vert \mathbf{A}\mathbf{x}-\mathbf{b} \vert\vert_2^2 + \lambda\vert\vert\mathbf{x}\vert\vert^2_2 .
 # \end{equation}
 # ```
 

docs/src/literate/examples/getting_started.jl

@@ -23,7 +23,7 @@ using RegularizedLeastSquares
 #   \underset{\mathbf{x}}{argmin} \frac{1}{2}\vert\vert \mathbf{A}\mathbf{x}-\mathbf{b} \vert\vert_2^2 + \mathbf{R(x)} .
 # \end{equation}
 # ```
-# where $\mathbf{A}$ is a linear operator, $\mathbf{y}$ is the measurement vector, and $\mathbf{R(x)}$ is an (optional) regularization term.
+# where $\mathbf{A}$ is a linear operator, $\mathbf{b}$ is the measurement vector, and $\mathbf{R(x)}$ is an (optional) regularization term.
 # The goal is to retrieve an approximation of the unknown vector $\mathbf{x}$. In this first exampel we will just work with simple random arrays. For more advanced examples, please refer to the examples.
 
 A = rand(32, 16)
@@ -41,11 +41,11 @@ isapprox(x, x_approx, rtol = 0.001)
 # The CGNR algorithm can solve optimzation problems of the form:
 # ```math
 # \begin{equation}
-#   \underset{\mathbf{x}}{argmin} \frac{1}{2}\vert\vert \mathbf{A}\mathbf{x}-\mathbf{b} \vert\vert_2^2 + \vert\vert\mathbf{x}\vert\vert^2_2 .
+#   \underset{\mathbf{x}}{argmin} \frac{1}{2}\vert\vert \mathbf{A}\mathbf{x}-\mathbf{b} \vert\vert_2^2 + \lambda\vert\vert\mathbf{x}\vert\vert^2_2 .
 # \end{equation}
 # ```
 
-# The corresponding solver can be built with the L2 regularization term:
+# The corresponding solver can be built with the $l^2_2$-regularization term:
 solver = createLinearSolver(CGNR, A; reg = L2Regularization(0.0001), iterations=32);
 x_approx = solve!(solver, b)
 isapprox(x, x_approx, rtol = 0.001)

docs/src/literate/howto/weighting.jl

@@ -11,7 +11,7 @@
 # In the following, we will solve a weighted least squares problem of the form:
 # ```math
 # \begin{equation}
-#   \underset{\mathbf{x}}{argmin} \frac{1}{2}\vert\vert \mathbf{A}\mathbf{x}-\mathbf{b} \vert\vert_\mathbf{W}^2 + \vert\vert\mathbf{x}\vert\vert^2_2 .
+#   \underset{\mathbf{x}}{argmin} \frac{1}{2}\vert\vert \mathbf{A}\mathbf{x}-\mathbf{b} \vert\vert_\mathbf{W}^2 + \lambda\vert\vert\mathbf{x}\vert\vert^2_2 .
 # \end{equation}
 # ```
 using RegularizedLeastSquares, LinearOperatorCollection, LinearAlgebra

docs/src/solvers.md

@@ -82,4 +82,5 @@ SolverVariant(A; kwargs...) = Solver(A, VariantState(kwargs...))
 
 function iterate(solver::Solver, state::VarianteState)
   # Custom iteration
-end
+end
+```