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16 changes: 7 additions & 9 deletions docs/src/tutorials/linear.md
Original file line number Diff line number Diff line change
Expand Up @@ -84,11 +84,10 @@ LinearSolve.jl specifically tests with the following cases:

!!! note


Choosing the most specific matrix structure that matches your specific system will give you the most performance.
Thus if your matrix is symmetric, specifically building with `Symmetric(A)` will be faster than simply using `A`,
and will generally lead to better automatic linear solver choices. Note that you can also choose the type for `b`,
but generally a dense vector will be the fastest here and many solvers will not support a sparse `b`.
Choosing the most specific matrix structure that matches your specific system will give you the most performance.
Thus if your matrix is symmetric, specifically building with `Symmetric(A)` will be faster than simply using `A`,
and will generally lead to better automatic linear solver choices. Note that you can also choose the type for `b`,
but generally a dense vector will be the fastest here and many solvers will not support a sparse `b`.

## Using Matrix-Free Operators via SciMLOperators.jl

Expand Down Expand Up @@ -160,7 +159,6 @@ mfopA * sol.u - b

!!! note


Note that not all methods can use a matrix-free operator. For example, `LS.LUFactorization()` requires a matrix. If you use an
invalid method, you will get an error. The methods particularly from KrylovJL are the ones preferred for these cases
(and are defaulted to).
Note that not all methods can use a matrix-free operator. For example, `LS.LUFactorization()` requires a matrix. If you use an
invalid method, you will get an error. The methods particularly from KrylovJL are the ones preferred for these cases
(and are defaulted to).