diff --git a/docs/src/api/solver_errors.md b/docs/src/api/solver_errors.md
index 7ce61cdb..3e59bc74 100644
--- a/docs/src/api/solver_errors.md
+++ b/docs/src/api/solver_errors.md
@@ -16,6 +16,9 @@ FullResidual
 
 FullResidualRecipe
 
+LSgradient
+
+LSgradientRecipe
 ```
 
 ## Exported Functions
diff --git a/src/RLinearAlgebra.jl b/src/RLinearAlgebra.jl
index c8706bc1..4afee156 100644
--- a/src/RLinearAlgebra.jl
+++ b/src/RLinearAlgebra.jl
@@ -56,6 +56,7 @@ export QRSolver, QRSolverRecipe
 export SolverError, SolverErrorRecipe
 export complete_error, compute_error
 export FullResidual, FullResidualRecipe
+export LSgradient, LSgradientRecipe
 
 # Export ApproximatorError types and functions
 export ApproximatorError, ApproximatorErrorRecipe
diff --git a/src/Solvers/ErrorMethods.jl b/src/Solvers/ErrorMethods.jl
index 93506d21..c5d45f59 100644
--- a/src/Solvers/ErrorMethods.jl
+++ b/src/Solvers/ErrorMethods.jl
@@ -116,3 +116,4 @@ end
 
 # Include error method files 
 include("ErrorMethods/full_residual.jl")
+include("ErrorMethods/LSgradient.jl")
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diff --git a/src/Solvers/ErrorMethods/LSgradient.jl b/src/Solvers/ErrorMethods/LSgradient.jl
new file mode 100644
index 00000000..c2e05470
--- /dev/null
+++ b/src/Solvers/ErrorMethods/LSgradient.jl
@@ -0,0 +1,41 @@
+"""
+    LSgradient <: SolverError
+
+A `SolverError` structure for computing the least-squares gradient,
+    ``\\nabla f(x) = A' (A x - b)``
+
+# Fields
+- None
+"""
+struct LSgradient <: SolverError end
+
+"""
+    LSgradientRecipe <: SolverErrorRecipe
+A `SolverErrorRecipe` structure for computing the gradient of least-squares objective.
+
+# Fields
+- `gradient::AbstractVector`, `A'r`.
+"""
+mutable struct LSgradientRecipe{V<:AbstractVector} <: SolverErrorRecipe
+    gradient::V
+end
+
+function complete_error(
+    error::LSgradient, 
+    solver::Solver, 
+    A::AbstractMatrix, 
+    b::AbstractVector
+)
+    gradient = zeros(size(A,2))
+    return LSgradientRecipe{typeof(b)}(gradient)
+end
+
+function compute_error(
+    error::LSgradientRecipe, 
+    solver::SolverRecipe, 
+    A::AbstractMatrix, 
+    b::AbstractVector
+)::Float64
+    mul!(error.gradient, A', solver.residual_vec, 1.0, 0.0) # grad = A'r
+    return norm(error.gradient)
+end
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diff --git a/test/Solvers/ErrorMethods/LSgradient.jl b/test/Solvers/ErrorMethods/LSgradient.jl
new file mode 100644
index 00000000..fd371275
--- /dev/null
+++ b/test/Solvers/ErrorMethods/LSgradient.jl
@@ -0,0 +1,84 @@
+module gradient_error 
+using Test, RLinearAlgebra, Random
+import LinearAlgebra: mul!, norm
+using ..FieldTest
+using ..ApproxTol
+Random.seed!(1232)
+
+mutable struct TestSolver <: Solver end
+
+mutable struct TestSolverRecipe <: SolverRecipe
+    residual_vec::AbstractVector
+end
+
+@testset "LS Gradient" begin
+    @testset "LS Gradient: SolverError" begin
+        # Verify Supertype
+        @test supertype(LSgradient) == SolverError 
+
+        # Verify fieldnames and types
+        @test fieldnames(LSgradient) == ()
+        @test fieldtypes(LSgradient) == ()
+        # Verify the internal constructor
+
+    end
+
+    @testset "LS Gradient: SolverErrorRecipe" begin
+        # Verify Supertype
+        @test supertype(LSgradientRecipe) ==  SolverErrorRecipe
+
+        # Verify fieldnames and types
+        @test fieldnames(LSgradientRecipe) == (:gradient,)
+        @test fieldtypes(LSgradientRecipe) == (AbstractVector,)
+    end
+
+    @testset "Residual: Complete error" begin
+        for type in [Float32, Float64, ComplexF32, ComplexF64] 
+            let n_rows = 4,
+                n_cols = 6,
+                A = rand(type, n_rows, n_cols),
+                b = rand(type, n_rows),
+                x = rand(type, n_cols),
+                r = A*x - b,
+                solver_rec = TestSolverRecipe(r),
+                error_rec = complete_error(LSgradient(), TestSolver(), A, b)
+
+                # Test the type
+                @test typeof(error_rec) == LSgradientRecipe{typeof(b)}
+                # Test type of residual vector
+                @test eltype(error_rec.gradient) == type
+                # Test residual vector to be all zeros
+                @test error_rec.gradient == zeros(type, n_cols)
+            end
+
+        end
+
+    end
+
+    @testset "Residual: Compute Error" begin
+        for type in [Float32, Float64] 
+            let n_rows = 4,
+                n_cols = 6,
+                A = rand(type, n_rows, n_cols),
+                b = rand(type, n_rows),
+                x = rand(type, n_cols),
+                r = A*x - b,
+                solver_rec = TestSolverRecipe(r),
+                solver = TestSolver(),
+                error_rec = complete_error(LSgradient(), TestSolver(), A, b)
+
+                # compute the error value
+                err_val = compute_error(error_rec, solver_rec, A, b)
+                # compute the gradient
+                res = A' * r
+                # compute norm squared of residual
+                @test norm(res) ≈ err_val
+            end
+
+        end
+
+    end
+
+end
+
+end
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