expand docstring

Author: lkdvos

src/interface/decompositions.jl

@@ -307,9 +307,21 @@ until convergence up to tolerance `tol`.
 """
     DefaultAlgorithm(; kwargs...)
 
-Algorithm sentinel that resolves to the default algorithm for a given function and input
-type at call time. Any keyword arguments stored in the instance are forwarded at runtime
-to [`select_algorithm`](@ref).
+Algorithm sentinel that resolves to the algorithm section procedures for a given function and input type at call time.
+This provides a unified approach for package developers to store keyword argument and direct algorithm inputs.
+Any keyword arguments stored in the instance are forwarded at runtime to [`select_algorithm`](@ref).
+
+For example, the following calls are equivalent:
+
+```julia
+A = rand(3, 3)
+
+# specifying keyword arguments
+Q, R = qr_compact(A; positive = true)
+
+# wrapping keyword arguments in DefaultAlgorithm
+alg = DefaultAlgorithm(; positive = true)
+Q, R = qr_compact(A; alg)
 """
 @algdef DefaultAlgorithm