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Fix two typos
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amontoison committed Oct 11, 2024
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4 changes: 2 additions & 2 deletions docs/src/matrix_free.md
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Expand Up @@ -166,7 +166,7 @@ For a function $u(x)$ discretized on a periodic grid with $n$ points, the FFT of
\hat{u}_k = \sum_{j=0}^{n-1} u_j e^{-i k x_j},
```

where $\hat{u}_k$ represents the Fourier coefficients for the frequency $k$, and $u_j$ is the value of $u$ at the grid point $x_j$ defined as $x_j = \frac{2 \pi j}{L} with period $L$.
where $\hat{u}_k$ represents the Fourier coefficients for the frequency $k$, and $u_j$ is the value of $u$ at the grid point $x_j$ defined as $x_j = \frac{2 \pi j}{L}$ with period $L$.
The inverse FFT (IFFT) reconstructs $u$ from its Fourier coefficients:

```math
Expand All @@ -192,7 +192,7 @@ This example consists of solving the 1D Poisson equation on a periodic domain $[
```

where $u(x)$ is the unknown solution, and $f(x)$ is the given source term.
We solve this equation using [FFTW.jl](https://github.com/JuliaMath/FFTW.jl) to compute the matrix-free action of the Laplacian within CG.
We solve this equation using [FFTW.jl](https://github.com/JuliaMath/FFTW.jl) to compute the matrix-free action of the Laplacian within the conjugate gradient solver.

```@example fft_poisson
using FFTW, Krylov, LinearAlgebra
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