Use LDLtFactorization for SymTridiagonal matrices

- Changed default algorithm selection for SymTridiagonal to use LDLtFactorization
- This caches the LDLT factorization for reuse in subsequent solves
- Addresses performance issue where ldlt was being recomputed on every solve

Author: claude

src/default.jl

@@ -142,11 +142,7 @@ function defaultalg(A::Tridiagonal, b, assump::OperatorAssumptions{Bool})
 end
 
 function defaultalg(A::SymTridiagonal, b, ::OperatorAssumptions{Bool})
-    @static if VERSION>=v"1.11"
-          DirectLdiv!()
-      else
-          DefaultLinearSolver(DefaultAlgorithmChoice.LUFactorization)
-      end
+    DefaultLinearSolver(DefaultAlgorithmChoice.LDLtFactorization)
 end
 function defaultalg(A::Bidiagonal, b, ::OperatorAssumptions{Bool})
     @static if VERSION>=v"1.11"