Update LDLFactorizations tutorial (#74)

Author: tmigot

tutorials/introduction-to-ldlfactorizations/index.jmd

@@ -75,3 +75,21 @@ LDL.r1 = 2 * ϵ # if any of the n_d first pivots |D[i]| < ϵ, then D[i] = sign(L
 LDL.r2 = -ϵ # if any of the n - n_d last pivots |D[i]| < ϵ, then D[i] = sign(LDL.r2) * max(abs(D[i] + LDL.r2), abs(LDL.r2))
 ldl_factorize!(Au, LDL)
 ```
+
+## Choosing the precision of the factorization
+
+It is possible to factorize a matrix in a different type than the type of its elements:
+
+```julia
+# with eltype(Au) == Float64
+LDL64 = ldl(Au) # factorization in eltype(Au) = Float64
+LDL32 = ldl(Au, Float32) # factorization in Float32
+```
+
+```julia
+# with eltype(Au) == Float64
+LDL64 = ldl_analyze(Au) # symbolic analysis in eltype(Au) = Float64
+LDL32 = ldl_analyze(Au, Float32) # symbolic analysis in Float32
+ldl_factorize!(Au, LDL64)
+ldl_factorize!(Au, LDL32)
+```