Add AMDGPU methods to documentation (#712)

* Add AMDGPU methods to documentation

- Added AMDGPUOffloadLUFactorization and AMDGPUOffloadQRFactorization to solver docs
- Added example usage in GPU tutorial section
- Documented requirement for AMDGPU.jl package

🤖 Generated with Claude Code

Co-Authored-By: Claude <[email protected]>

* Update docs/src/tutorials/gpu.md

---------

Co-authored-by: Claude <[email protected]>

Author: ChrisRackauckas

docs/src/solvers/solvers.md

@@ -238,6 +238,19 @@ The following are non-standard GPU factorization routines.
 CudaOffloadFactorization
 ```
 
+### AMDGPU.jl
+
+The following are GPU factorization routines for AMD GPUs using the ROCm stack.
+
+!!! note
+    
+    Using these solvers requires adding the package AMDGPU.jl, i.e. `using AMDGPU`
+
+```@docs
+AMDGPUOffloadLUFactorization
+AMDGPUOffloadQRFactorization
+```
+
 ### CUSOLVERRF.jl
 
 !!! note

docs/src/tutorials/gpu.md

@@ -39,8 +39,18 @@ sol.u
 This computation can be moved to the GPU by the following:
 
 ```julia
-using CUDA # Add the GPU library
-sol = LS.solve(prob, LS.CudaOffloadFactorization())
+using CUDA # Add the GPU library for NVIDIA GPUs
+sol = LS.solve(prob, LS.CudaOffloadLUFactorization())
+sol.u
+```
+
+For AMD GPUs, you can use the AMDGPU.jl package:
+
+```julia
+using AMDGPU # Add the GPU library for AMD GPUs
+sol = LS.solve(prob, LS.AMDGPUOffloadLUFactorization())  # LU factorization
+# or
+sol = LS.solve(prob, LS.AMDGPUOffloadQRFactorization())  # QR factorization
 sol.u
 ```