diff --git a/ext/MatrixAlgebraKitMooncakeExt/MatrixAlgebraKitMooncakeExt.jl b/ext/MatrixAlgebraKitMooncakeExt/MatrixAlgebraKitMooncakeExt.jl
index c2814ef6..f6feda8b 100644
--- a/ext/MatrixAlgebraKitMooncakeExt/MatrixAlgebraKitMooncakeExt.jl
+++ b/ext/MatrixAlgebraKitMooncakeExt/MatrixAlgebraKitMooncakeExt.jl
@@ -163,9 +163,9 @@ for (f!, f, f_full, pb, adj) in (
     end
 end
 
-for (f, pb, adj) in (
-        (:eig_trunc, :eig_trunc_pullback!, :eig_trunc_adjoint),
-        (:eigh_trunc, :eigh_trunc_pullback!, :eigh_trunc_adjoint),
+for (f, f_ne, pb, adj) in (
+        (:eig_trunc, :eig_trunc_no_error, :eig_trunc_pullback!, :eig_trunc_adjoint),
+        (:eigh_trunc, :eigh_trunc_no_error, :eigh_trunc_pullback!, :eigh_trunc_adjoint),
     )
     @eval begin
         @is_primitive Mooncake.DefaultCtx Mooncake.ReverseMode Tuple{typeof($f), Any, MatrixAlgebraKit.AbstractAlgorithm}
@@ -192,6 +192,29 @@ for (f, pb, adj) in (
             end
             return output_codual, $adj
         end
+        @is_primitive Mooncake.DefaultCtx Mooncake.ReverseMode Tuple{typeof($f_ne), Any, MatrixAlgebraKit.AbstractAlgorithm}
+        function Mooncake.rrule!!(::CoDual{typeof($f_ne)}, A_dA::CoDual, alg_dalg::CoDual)
+            # compute primal
+            A, dA = arrayify(A_dA)
+            alg = Mooncake.primal(alg_dalg)
+            output = $f_ne(A, alg)
+            # fdata call here is necessary to convert complicated Tangent type (e.g. of a Diagonal
+            # of ComplexF32) into the correct **forwards** data type (since we are now in the forward
+            # pass). For many types this is done automatically when the forward step returns, but
+            # not for nested structs with various fields (like Diagonal{Complex})
+            output_codual = CoDual(output, Mooncake.fdata(Mooncake.zero_tangent(output)))
+            function $adj(::NoRData)
+                Dtrunc, Vtrunc = Mooncake.primal(output_codual)
+                dDtrunc_, dVtrunc_ = Mooncake.tangent(output_codual)
+                D, dD = arrayify(Dtrunc, dDtrunc_)
+                V, dV = arrayify(Vtrunc, dVtrunc_)
+                $pb(dA, A, (D, V), (dD, dV))
+                MatrixAlgebraKit.zero!(dD)
+                MatrixAlgebraKit.zero!(dV)
+                return NoRData(), NoRData(), NoRData()
+            end
+            return output_codual, $adj
+        end
     end
 end
 
diff --git a/src/MatrixAlgebraKit.jl b/src/MatrixAlgebraKit.jl
index 85cfc633..2178d41a 100644
--- a/src/MatrixAlgebraKit.jl
+++ b/src/MatrixAlgebraKit.jl
@@ -18,10 +18,10 @@ export qr_compact, qr_full, qr_null, lq_compact, lq_full, lq_null
 export qr_compact!, qr_full!, qr_null!, lq_compact!, lq_full!, lq_null!
 export svd_compact, svd_full, svd_vals, svd_trunc, svd_trunc_no_error
 export svd_compact!, svd_full!, svd_vals!, svd_trunc!, svd_trunc_no_error!
-export eigh_full, eigh_vals, eigh_trunc
-export eigh_full!, eigh_vals!, eigh_trunc!
-export eig_full, eig_vals, eig_trunc
-export eig_full!, eig_vals!, eig_trunc!
+export eigh_full, eigh_vals, eigh_trunc, eigh_trunc_no_error
+export eigh_full!, eigh_vals!, eigh_trunc!, eigh_trunc_no_error!
+export eig_full, eig_vals, eig_trunc, eig_trunc_no_error
+export eig_full!, eig_vals!, eig_trunc!, eig_trunc_no_error!
 export gen_eig_full, gen_eig_vals
 export gen_eig_full!, gen_eig_vals!
 export schur_full, schur_vals
diff --git a/src/implementations/eig.jl b/src/implementations/eig.jl
index 9b14167c..5a0dd679 100644
--- a/src/implementations/eig.jl
+++ b/src/implementations/eig.jl
@@ -4,7 +4,7 @@ function copy_input(::typeof(eig_full), A::AbstractMatrix)
     return copy!(similar(A, float(eltype(A))), A)
 end
 copy_input(::typeof(eig_vals), A) = copy_input(eig_full, A)
-copy_input(::typeof(eig_trunc), A) = copy_input(eig_full, A)
+copy_input(::Union{typeof(eig_trunc), typeof(eig_trunc_no_error)}, A) = copy_input(eig_full, A)
 
 copy_input(::typeof(eig_full), A::Diagonal) = copy(A)
 
@@ -65,7 +65,7 @@ function initialize_output(::typeof(eig_vals!), A::AbstractMatrix, ::AbstractAlg
     D = similar(A, Tc, n)
     return D
 end
-function initialize_output(::typeof(eig_trunc!), A, alg::TruncatedAlgorithm)
+function initialize_output(::Union{typeof(eig_trunc!), typeof(eig_trunc_no_error!)}, A, alg::TruncatedAlgorithm)
     return initialize_output(eig_full!, A, alg.alg)
 end
 
@@ -121,6 +121,12 @@ function eig_trunc!(A, DV, alg::TruncatedAlgorithm)
     return DVtrunc..., truncation_error!(diagview(D), ind)
 end
 
+function eig_trunc_no_error!(A, DV, alg::TruncatedAlgorithm)
+    D, V = eig_full!(A, DV, alg.alg)
+    DVtrunc, ind = truncate(eig_trunc!, (D, V), alg.trunc)
+    return DVtrunc
+end
+
 # Diagonal logic
 # --------------
 function eig_full!(A::Diagonal, (D, V)::Tuple{Diagonal, Diagonal}, alg::DiagonalAlgorithm)
diff --git a/src/implementations/eigh.jl b/src/implementations/eigh.jl
index a45300dc..40f2c557 100644
--- a/src/implementations/eigh.jl
+++ b/src/implementations/eigh.jl
@@ -4,7 +4,7 @@ function copy_input(::typeof(eigh_full), A::AbstractMatrix)
     return copy!(similar(A, float(eltype(A))), A)
 end
 copy_input(::typeof(eigh_vals), A) = copy_input(eigh_full, A)
-copy_input(::typeof(eigh_trunc), A) = copy_input(eigh_full, A)
+copy_input(::Union{typeof(eigh_trunc), typeof(eigh_trunc_no_error)}, A) = copy_input(eigh_full, A)
 
 copy_input(::typeof(eigh_full), A::Diagonal) = copy(A)
 
@@ -74,7 +74,7 @@ function initialize_output(::typeof(eigh_vals!), A::AbstractMatrix, ::AbstractAl
     D = similar(A, real(eltype(A)), n)
     return D
 end
-function initialize_output(::typeof(eigh_trunc!), A, alg::TruncatedAlgorithm)
+function initialize_output(::Union{typeof(eigh_trunc!), typeof(eigh_trunc_no_error!)}, A, alg::TruncatedAlgorithm)
     return initialize_output(eigh_full!, A, alg.alg)
 end
 
@@ -135,6 +135,12 @@ function eigh_trunc!(A, DV, alg::TruncatedAlgorithm)
     return DVtrunc..., truncation_error!(diagview(D), ind)
 end
 
+function eigh_trunc_no_error!(A, DV, alg::TruncatedAlgorithm)
+    D, V = eigh_full!(A, DV, alg.alg)
+    DVtrunc, ind = truncate(eigh_trunc!, (D, V), alg.trunc)
+    return DVtrunc
+end
+
 # Diagonal logic
 # --------------
 function eigh_full!(A::Diagonal, DV, alg::DiagonalAlgorithm)
diff --git a/src/interface/eig.jl b/src/interface/eig.jl
index 28b5c69c..bb111c01 100644
--- a/src/interface/eig.jl
+++ b/src/interface/eig.jl
@@ -27,7 +27,8 @@ and the diagonal matrix `D` contains the associated eigenvalues.
 !!! note
 $(docs_eig_note)
 
-See also [`eig_vals(!)`](@ref eig_vals) and [`eig_trunc(!)`](@ref eig_trunc).
+See also [`eig_vals(!)`](@ref eig_vals), [`eig_trunc_no_error`](@ref eig_trunc_no_error)
+and [`eig_trunc(!)`](@ref eig_trunc).
 """
 @functiondef eig_full
 
@@ -79,11 +80,63 @@ truncation strategy is already embedded in the algorithm.
 !!! note
 $docs_eig_note
 
-See also [`eig_full(!)`](@ref eig_full), [`eig_vals(!)`](@ref eig_vals), and
-[Truncations](@ref) for more information on truncation strategies.
+See also [`eig_full(!)`](@ref eig_full), [`eig_vals(!)`](@ref eig_vals),
+[`eig_trunc_no_error!`](@ref eig_trunc_no_error) and [Truncations](@ref)
+for more information on truncation strategies.
 """
 @functiondef eig_trunc
 
+"""
+    eig_trunc_no_error(A; [trunc], kwargs...) -> D, V
+    eig_trunc_no_error(A, alg::AbstractAlgorithm) -> D, V
+    eig_trunc_no_error!(A, [DV]; [trunc], kwargs...) -> D, V
+    eig_trunc_no_error!(A, [DV], alg::AbstractAlgorithm) -> D, V
+
+Compute a partial or truncated eigenvalue decomposition of the matrix `A`,
+such that `A * V ≈ V * D`, where the (possibly rectangular) matrix `V` contains 
+a subset of eigenvectors and the diagonal matrix `D` contains the associated eigenvalues,
+selected according to a truncation strategy. The truncation error is *not* returned.
+
+## Truncation
+The truncation strategy can be controlled via the `trunc` keyword argument. This can be
+either a `NamedTuple` or a [`TruncationStrategy`](@ref). If `trunc` is not provided or
+nothing, all values will be kept.
+
+### `trunc::NamedTuple`
+The supported truncation keyword arguments are:
+
+$docs_truncation_kwargs
+
+### `trunc::TruncationStrategy`
+For more control, a truncation strategy can be supplied directly.
+By default, MatrixAlgebraKit supplies the following:
+
+$docs_truncation_strategies
+
+## Keyword Arguments
+Other keyword arguments are passed to the algorithm selection procedure. If no explicit
+`alg` is provided, these keywords are used to select and configure the algorithm through
+[`MatrixAlgebraKit.select_algorithm`](@ref). The remaining keywords after algorithm
+selection are passed to the algorithm constructor. See [`MatrixAlgebraKit.default_algorithm`](@ref)
+for the default algorithm selection behavior.
+
+When `alg` is a [`TruncatedAlgorithm`](@ref), the `trunc` keyword cannot be specified as the
+truncation strategy is already embedded in the algorithm.
+
+!!! note
+    The bang method `eig_trunc!` optionally accepts the output structure and
+    possibly destroys the input matrix `A`. Always use the return value of the function
+    as it may not always be possible to use the provided `DV` as output.
+
+!!! note
+$docs_eig_note
+
+See also [`eig_full(!)`](@ref eig_full), [`eig_vals(!)`](@ref eig_vals),
+[`eig_trunc(!)`](@ref eig_trunc) and [Truncations](@ref) for more
+information on truncation strategies.
+"""
+@functiondef eig_trunc_no_error
+
 """
     eig_vals(A; kwargs...) -> D
     eig_vals(A, alg::AbstractAlgorithm) -> D
@@ -121,13 +174,15 @@ for f in (:eig_full!, :eig_vals!)
     end
 end
 
-function select_algorithm(::typeof(eig_trunc!), A, alg; trunc = nothing, kwargs...)
-    if alg isa TruncatedAlgorithm
-        isnothing(trunc) ||
-            throw(ArgumentError("`trunc` can't be specified when `alg` is a `TruncatedAlgorithm`"))
-        return alg
-    else
-        alg_eig = select_algorithm(eig_full!, A, alg; kwargs...)
-        return TruncatedAlgorithm(alg_eig, select_truncation(trunc))
+for f in (:eig_trunc!, :eig_trunc_no_error!)
+    @eval function select_algorithm(::typeof($f), A, alg; trunc = nothing, kwargs...)
+        if alg isa TruncatedAlgorithm
+            isnothing(trunc) ||
+                throw(ArgumentError("`trunc` can't be specified when `alg` is a `TruncatedAlgorithm`"))
+            return alg
+        else
+            alg_eig = select_algorithm(eig_full!, A, alg; kwargs...)
+            return TruncatedAlgorithm(alg_eig, select_truncation(trunc))
+        end
     end
 end
diff --git a/src/interface/eigh.jl b/src/interface/eigh.jl
index 97f8f95c..42c7f9f3 100644
--- a/src/interface/eigh.jl
+++ b/src/interface/eigh.jl
@@ -84,11 +84,63 @@ truncation strategy is already embedded in the algorithm.
 !!! note
 $(docs_eigh_note)
 
-See also [`eigh_full(!)`](@ref eigh_full), [`eigh_vals(!)`](@ref eigh_vals), and
-[Truncations](@ref) for more information on truncation strategies.
+See also [`eigh_full(!)`](@ref eigh_full), [`eigh_vals(!)`](@ref eigh_vals),
+[`eigh_trunc_no_error(!)`](@ref eigh_trunc_no_error) and [Truncations](@ref)
+for more information on truncation strategies.
 """
 @functiondef eigh_trunc
 
+"""
+    eigh_trunc_no_error(A; [trunc], kwargs...) -> D, V
+    eigh_trunc_no_error(A, alg::AbstractAlgorithm) -> D, V
+    eigh_trunc_no_error!(A, [DV]; [trunc], kwargs...) -> D, V
+    eigh_trunc_no_error!(A, [DV], alg::AbstractAlgorithm) -> D, V
+
+Compute a partial or truncated eigenvalue decomposition of the symmetric or hermitian matrix
+`A`, such that `A * V ≈ V * D`, where the isometric matrix `V` contains a subset of the
+orthogonal eigenvectors and the real diagonal matrix `D` contains the associated eigenvalues,
+selected according to a truncation strategy.  The function does *not* returns the truncation error. 
+
+## Truncation
+The truncation strategy can be controlled via the `trunc` keyword argument. This can be
+either a `NamedTuple` or a [`TruncationStrategy`](@ref). If `trunc` is not provided or
+nothing, all values will be kept.
+
+### `trunc::NamedTuple`
+The supported truncation keyword arguments are:
+
+$docs_truncation_kwargs
+
+### `trunc::TruncationStrategy`
+For more control, a truncation strategy can be supplied directly.
+By default, MatrixAlgebraKit supplies the following:
+
+$docs_truncation_strategies
+
+## Keyword arguments
+Other keyword arguments are passed to the algorithm selection procedure. If no explicit
+`alg` is provided, these keywords are used to select and configure the algorithm through
+[`MatrixAlgebraKit.select_algorithm`](@ref). The remaining keywords after algorithm
+selection are passed to the algorithm constructor. See [`MatrixAlgebraKit.default_algorithm`](@ref)
+for the default algorithm selection behavior.
+
+When `alg` is a [`TruncatedAlgorithm`](@ref), the `trunc` keyword cannot be specified as the
+truncation strategy is already embedded in the algorithm.
+
+!!! note
+    The bang method `eigh_trunc!` optionally accepts the output structure and
+    possibly destroys the input matrix `A`. Always use the return value of the function
+    as it may not always be possible to use the provided `DV` as output.
+
+!!! note
+$(docs_eigh_note)
+
+See also [`eigh_full(!)`](@ref eigh_full), [`eigh_vals(!)`](@ref eigh_vals),
+[`eigh_trunc(!)`](@ref eig_trunc), and [Truncations](@ref) for more information
+on truncation strategies.
+"""
+@functiondef eigh_trunc_no_error
+
 """
     eigh_vals(A; kwargs...) -> D
     eigh_vals(A, alg::AbstractAlgorithm) -> D
@@ -128,13 +180,15 @@ for f in (:eigh_full!, :eigh_vals!)
     end
 end
 
-function select_algorithm(::typeof(eigh_trunc!), A, alg; trunc = nothing, kwargs...)
-    if alg isa TruncatedAlgorithm
-        isnothing(trunc) ||
-            throw(ArgumentError("`trunc` can't be specified when `alg` is a `TruncatedAlgorithm`"))
-        return alg
-    else
-        alg_eig = select_algorithm(eigh_full!, A, alg; kwargs...)
-        return TruncatedAlgorithm(alg_eig, select_truncation(trunc))
+for f in (:eigh_trunc!, :eigh_trunc_no_error!)
+    @eval function select_algorithm(::typeof($f), A, alg; trunc = nothing, kwargs...)
+        if alg isa TruncatedAlgorithm
+            isnothing(trunc) ||
+                throw(ArgumentError("`trunc` can't be specified when `alg` is a `TruncatedAlgorithm`"))
+            return alg
+        else
+            alg_eig = select_algorithm(eigh_full!, A, alg; kwargs...)
+            return TruncatedAlgorithm(alg_eig, select_truncation(trunc))
+        end
     end
 end
diff --git a/test/eig.jl b/test/eig.jl
index 6da6d72c..d709bd20 100644
--- a/test/eig.jl
+++ b/test/eig.jl
@@ -64,6 +64,11 @@ end
         @test A * V3 ≈ V3 * D3
         @test ϵ3 ≈ norm(view(D₀, (r + 1):m)) atol = atol
 
+        s = 1 - sqrt(eps(real(T)))
+        trunc = truncerror(; atol = s * norm(@view(D₀[r:end]), 1), p = 1)
+        D4, V4 = @constinferred eig_trunc_no_error(A; alg, trunc)
+        @test length(diagview(D4)) == r
+        @test A * V4 ≈ V4 * D4
         # trunctol keeps order, truncrank might not
         # test for same subspace
         @test V1 * ((V1' * V1) \ (V1' * V2)) ≈ V2
@@ -90,6 +95,10 @@ end
     D3, V3, ϵ3 = @constinferred eig_trunc(A; alg)
     @test diagview(D3) ≈ diagview(D)[1:2]
     @test ϵ3 ≈ norm(diagview(D)[3:4]) atol = atol
+
+    alg = TruncatedAlgorithm(LAPACK_Simple(), truncerror(; atol = 0.2, p = 1))
+    D4, V4 = @constinferred eig_trunc_no_error(A; alg)
+    @test diagview(D4) ≈ diagview(D)[1:2]
 end
 
 @testset "eig for Diagonal{$T}" for T in (BLASFloats..., GenericFloats...)
@@ -113,4 +122,9 @@ end
     D2, V2, ϵ2 = @constinferred eig_trunc(A2; alg)
     @test diagview(D2) ≈ diagview(A2)[1:2]
     @test ϵ2 ≈ norm(diagview(A2)[3:4]) atol = atol
+
+    A3 = Diagonal(T[0.9, 0.3, 0.1, 0.01])
+    alg = TruncatedAlgorithm(DiagonalAlgorithm(), truncrank(2))
+    D3, V3 = @constinferred eig_trunc_no_error(A3; alg)
+    @test diagview(D3) ≈ diagview(A3)[1:2]
 end
diff --git a/test/eigh.jl b/test/eigh.jl
index 92b0f3a0..3b711c5b 100644
--- a/test/eigh.jl
+++ b/test/eigh.jl
@@ -73,6 +73,12 @@ end
         @test A * V3 ≈ V3 * D3
         @test ϵ3 ≈ norm(view(D₀, (r + 1):m)) atol = atol
 
+        s = 1 - sqrt(eps(real(T)))
+        trunc = truncerror(; atol = s * norm(@view(D₀[r:end]), 1), p = 1)
+        D4, V4 = @constinferred eigh_trunc_no_error(A; alg, trunc)
+        @test length(diagview(D4)) == r
+        @test A * V4 ≈ V4 * D4
+
         # test for same subspace
         @test V1 * (V1' * V2) ≈ V2
         @test V2 * (V2' * V1) ≈ V1
@@ -99,6 +105,10 @@ end
     D3, V3, ϵ3 = @constinferred eigh_trunc(A; alg)
     @test diagview(D3) ≈ diagview(D)[1:2]
     @test ϵ3 ≈ norm(diagview(D)[3:4]) atol = atol
+
+    alg = TruncatedAlgorithm(LAPACK_QRIteration(), truncerror(; atol = 0.2))
+    D4, V4 = @constinferred eigh_trunc_no_error(A; alg)
+    @test diagview(D4) ≈ diagview(D)[1:2]
 end
 
 @testset "eigh for Diagonal{$T}" for T in (BLASFloats..., GenericFloats...)
@@ -123,4 +133,9 @@ end
     D2, V2, ϵ2 = @constinferred eigh_trunc(A2; alg)
     @test diagview(D2) ≈ diagview(A2)[1:2]
     @test ϵ2 ≈ norm(diagview(A2)[3:4]) atol = atol
+
+    A3 = Diagonal(T[0.9, 0.3, 0.1, 0.01])
+    alg = TruncatedAlgorithm(DiagonalAlgorithm(), truncrank(3))
+    D3, V3 = @constinferred eigh_trunc_no_error(A3; alg)
+    @test diagview(D3) ≈ diagview(A3)[1:3]
 end
diff --git a/test/mooncake.jl b/test/mooncake.jl
index a47bbb8d..c3917847 100644
--- a/test/mooncake.jl
+++ b/test/mooncake.jl
@@ -276,6 +276,9 @@ end
                 dDVtrunc = Mooncake.build_tangent(typeof((ΔDtrunc, ΔVtrunc, zero(real(T)))), dDtrunc, dVtrunc, zero(real(T)))
                 Mooncake.TestUtils.test_rule(rng, eig_trunc, A, truncalg; mode = Mooncake.ReverseMode, output_tangent = dDVtrunc, atol = atol, rtol = rtol, is_primitive = false)
                 test_pullbacks_match(rng, eig_trunc!, eig_trunc, A, (D, V), (ΔD2, ΔV), truncalg; rdata = (Mooncake.NoRData(), Mooncake.NoRData(), zero(real(T))))
+                dDVtrunc = Mooncake.build_tangent(typeof((ΔDtrunc, ΔVtrunc)), dDtrunc, dVtrunc)
+                Mooncake.TestUtils.test_rule(rng, eig_trunc_no_error, A, truncalg; mode = Mooncake.ReverseMode, output_tangent = dDVtrunc, atol = atol, rtol = rtol, is_primitive = false)
+                test_pullbacks_match(rng, eig_trunc_no_error!, eig_trunc_no_error, A, (D, V), (ΔD2, ΔV), truncalg)
             end
             truncalg = TruncatedAlgorithm(alg, truncrank(5; by = real))
             ind = MatrixAlgebraKit.findtruncated(Ddiag, truncalg.trunc)
@@ -288,6 +291,9 @@ end
             dDVtrunc = Mooncake.build_tangent(typeof((ΔDtrunc, ΔVtrunc, zero(real(T)))), dDtrunc, dVtrunc, zero(real(T)))
             Mooncake.TestUtils.test_rule(rng, eig_trunc, A, truncalg; mode = Mooncake.ReverseMode, output_tangent = dDVtrunc, atol = atol, rtol = rtol, is_primitive = false)
             test_pullbacks_match(rng, eig_trunc!, eig_trunc, A, (D, V), (ΔD2, ΔV), truncalg; rdata = (Mooncake.NoRData(), Mooncake.NoRData(), zero(real(T))))
+            dDVtrunc = Mooncake.build_tangent(typeof((ΔDtrunc, ΔVtrunc)), dDtrunc, dVtrunc)
+            Mooncake.TestUtils.test_rule(rng, eig_trunc_no_error, A, truncalg; mode = Mooncake.ReverseMode, output_tangent = dDVtrunc, atol = atol, rtol = rtol, is_primitive = false)
+            test_pullbacks_match(rng, eig_trunc_no_error!, eig_trunc_no_error, A, (D, V), (ΔD2, ΔV), truncalg)
         end
     end
 end