Update solvers.md

Author: ChrisRackauckas

docs/src/solvers/solvers.md

@@ -38,14 +38,29 @@ like CUDA.
 ### Base.LinearAlgebra
 
 These overloads tend to work for many array types, such as `CuArrays` for GPU-accelerated
-solving, using the overloads provided by the respective packages.
+solving, using the overloads provided by the respective packages. Given that this can be
+customized per-package, details given below describe a subset of important arrays
+(`Matrix`, `SparseMatrixCSC`, `CuMatrix`, etc.) 
 
 - `LUFactorization(pivot=LinearAlgebra.RowMaximum())`: Julia's built in `lu`.
-  Uses the current BLAS implementation of the user's computer.
+  - On dense matrices this uses the current BLAS implementation of the user's computer
+    which by default is OpenBLAS but will use MKL if the user does `using MKL` in their
+    system. 
+  - On sparse matrices this will use UMFPACK from SuiteSparse. Note that this will not
+    cache the symbolic factorization.
+  - On CuMatrix it will use a CUDA-accelerated LU from CuSolver.
+  - On BandedMatrix and BlockBandedMatrix it will use a banded LU.
 - `QRFactorization(pivot=LinearAlgebra.NoPivot(),blocksize=16)`: Julia's built in `qr`.
-  Uses the current BLAS implementation of the user's computer.
+  - On dense matrices this uses the current BLAS implementation of the user's computer
+    which by default is OpenBLAS but will use MKL if the user does `using MKL` in their
+    system. 
+  - On sparse matrices this will use SPQR from SuiteSparse
+  - On CuMatrix it will use a CUDA-accelerated QR from CuSolver.
+  - On BandedMatrix and BlockBandedMatrix it will use a banded QR.
 - `SVDFactorization(full=false,alg=LinearAlgebra.DivideAndConquer())`: Julia's built in `svd`.
-  Uses the current BLAS implementation of the user's computer.
+  - On dense matrices this uses the current BLAS implementation of the user's computer
+    which by default is OpenBLAS but will use MKL if the user does `using MKL` in their
+    system. 
 - `GenericFactorization(fact_alg)`: Constructs a linear solver from a generic
   factorization algorithm `fact_alg` which complies with the Base.LinearAlgebra
   factorization API.