diff --git a/docs/src/api/solver_errors.md b/docs/src/api/solver_errors.md
index 7ce61cdb..49804cdd 100644
--- a/docs/src/api/solver_errors.md
+++ b/docs/src/api/solver_errors.md
@@ -16,6 +16,9 @@ FullResidual
 
 FullResidualRecipe
 
+CompressedResidual
+
+CompressedResidualRecipe
 ```
 
 ## Exported Functions
diff --git a/src/RLinearAlgebra.jl b/src/RLinearAlgebra.jl
index a0c8b9a0..53406a81 100644
--- a/src/RLinearAlgebra.jl
+++ b/src/RLinearAlgebra.jl
@@ -43,7 +43,7 @@ export LQSolver, LQSolverRecipe
 # Export SolverError types and functions
 export SolverError, SolverErrorRecipe
 export complete_error, compute_error
-export FullResidual, FullResidualRecipe
+export FullResidual, FullResidualRecipe, CompressedResidual, CompressedResidualRecipe
 
 # Export ApproximatorError types and functions
 export ApproximatorError, ApproximatorErrorRecipe
diff --git a/src/Solvers/ErrorMethods.jl b/src/Solvers/ErrorMethods.jl
index 93506d21..ee41b877 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/compressed_residual.jl")
diff --git a/src/Solvers/ErrorMethods/compressed_residual.jl b/src/Solvers/ErrorMethods/compressed_residual.jl
new file mode 100644
index 00000000..7b2cc489
--- /dev/null
+++ b/src/Solvers/ErrorMethods/compressed_residual.jl
@@ -0,0 +1,54 @@
+"""
+    CompressedResidual <: ErrorRecipe
+
+A structure for the compressed residual, `Sb-SAx`.
+
+# Fields
+- None
+"""
+struct CompressedResidual <: SolverError
+
+end
+
+"""
+    CompressedResidualRecipe <: ErrorRecipe
+
+A structure for the compressed residual, `Sb-SAx`.
+
+# Fields
+- `residual::AbstractVector`, a container for the compressed residual, `Sb-SAx`.
+- `residual_view::SubArray`, a view of the residual container to handle varying compression
+    sizes.
+"""
+mutable struct CompressedResidualRecipe{V<:AbstractVector, S<:SubArray} <: SolverErrorRecipe
+    residual::V
+    residual_view::S
+end
+
+function complete_error(
+    error::CompressedResidual, 
+    solver::Solver,
+    A::AbstractMatrix, 
+    b::AbstractVector
+)
+    residual = zeros(eltype(A), size(b,1))
+    residual_view = view(residual, 1:1)
+    return CompressedResidualRecipe{typeof(residual),typeof(residual_view)}(
+        residual, 
+        residual_view
+    )
+
+end
+
+function compute_error(
+        error::CompressedResidualRecipe, 
+        solver::SolverRecipe, 
+        A::AbstractMatrix, 
+        b::AbstractVector
+    )::Float64
+    rows_s = size(solver.compressor, 1)
+    error.residual_view = view(error.residual, 1:rows_s)
+    copyto!(error.residual_view, solver.vec_view)
+    mul!(error.residual_view, solver.mat_view, solver.solution_vec, -1.0, 1.0)
+    return norm(error.residual_view)
+end
diff --git a/test/Solvers/ErrorMethods/compressed_residual.jl b/test/Solvers/ErrorMethods/compressed_residual.jl
new file mode 100644
index 00000000..73b34781
--- /dev/null
+++ b/test/Solvers/ErrorMethods/compressed_residual.jl
@@ -0,0 +1,107 @@
+module compressed_residual_error 
+using Test, RLinearAlgebra, Random
+import LinearAlgebra: mul!, norm
+using ..FieldTest
+using ..ApproxTol
+Random.seed!(1232)
+
+###############################
+# Test Solver Structures
+###############################
+mutable struct TestSolver <: Solver end
+
+mutable struct TestSolverRecipe <: SolverRecipe
+    compressor::AbstractMatrix
+    vec_view::SubArray
+    mat_view::SubArray
+    solution_vec::AbstractVector
+end
+
+
+@testset "Compressed Residual" begin
+    @testset "Compressed Residual: SolverError" begin
+        # Verify Supertype
+        @test supertype(CompressedResidual) == SolverError 
+
+        # Verify fieldnames and types
+        @test fieldnames(CompressedResidual) == ()
+        @test fieldtypes(CompressedResidual) == ()
+        # Verify the internal constructor
+
+    end
+
+    @testset "Compressed Residual: SolverErrorRecipe" begin
+        # Verify Supertype
+        @test supertype(CompressedResidualRecipe) ==  SolverErrorRecipe
+
+        # Verify fieldnames and types
+        @test fieldnames(CompressedResidualRecipe) == (:residual, :residual_view)
+        @test fieldtypes(CompressedResidualRecipe) == (AbstractVector, SubArray)
+    end
+
+    @testset "Compressed Residual: Complete error" begin
+        for type in [Float32, Float64, ComplexF32, ComplexF64] 
+            let n_rows = 4,
+                n_cols = 3,
+                comp_dim = 2,
+                S = ones(type, n_rows, n_cols),
+                A = ones(type, n_rows, n_cols),
+                b = ones(type, n_rows),
+                x = ones(type, n_cols),
+                error_rec = complete_error(CompressedResidual(), TestSolver(), A, b)
+
+                # Test the type
+                @test typeof(error_rec) == CompressedResidualRecipe{
+                    Vector{type}, 
+                    SubArray{type, 1, Vector{type}, Tuple{UnitRange{Int64}}, true}
+                }
+                # Test type of residual vector
+                @test eltype(error_rec.residual) == type
+                # Test residual vector to be all zeros
+                @test error_rec.residual == zeros(type, n_rows)
+            end
+
+        end
+
+    end
+
+    @testset "Compressed Residual: Compute Error" begin
+        for type in [Float32, Float64, ComplexF32, ComplexF64] 
+            let n_rows = 4,
+                n_cols = 3,
+                comp_dim = 2,
+                A = ones(type, n_rows, n_cols),
+                S = ones(type, comp_dim, n_rows),
+                b = ones(type, n_rows),
+                x = ones(type, n_cols),
+                Sb = S * b,
+                SA = S * A
+                solver_rec = TestSolverRecipe(
+                    S,
+                    view(Sb, 1:comp_dim),
+                    view(SA, 1:comp_dim, 1:n_cols), 
+                    x 
+                )
+
+                error_rec = complete_error(
+                    CompressedResidual(), 
+                    TestSolver(), 
+                    A, 
+                    b
+                )
+
+                # compute the error value
+                err_val = compute_error(error_rec, solver_rec, A, b)
+                # compute the residual
+                res = Sb - SA * x
+                # compute norm squared of residual
+                @test norm(res) ≈ err_val
+            end
+
+        end
+
+    end
+
+end
+
+end