diff --git a/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl b/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl
index 0bdb10497..4a80ae0fd 100644
--- a/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl
+++ b/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl
@@ -6,9 +6,9 @@ using MatrixAlgebraKit: one!, zero!, uppertriangular!, lowertriangular!
 using MatrixAlgebraKit: diagview, sign_safe
 using MatrixAlgebraKit: ROCSOLVER, LQViaTransposedQR, TruncationStrategy, NoTruncation, TruncationByValue, AbstractAlgorithm
 using MatrixAlgebraKit: default_qr_algorithm, default_lq_algorithm, default_svd_algorithm, default_eigh_algorithm
-import MatrixAlgebraKit: geqrf!, ungqr!, unmqr!, gesvd!, gesvdj!
+import MatrixAlgebraKit: geqrf!, ungqr!, unmqr!, gesvd!, gesvdx!, gesvdj!
 import MatrixAlgebraKit: heevj!, heevd!, heev!, heevx!
-import MatrixAlgebraKit: _sylvester, svd_rank, svd_pullback!
+import MatrixAlgebraKit: _sylvester, svd_rank, svd_pullback!, complete_svd_basis!
 using AMDGPU
 using LinearAlgebra
 using LinearAlgebra: BlasFloat
@@ -28,7 +28,7 @@ for f in (:geqrf!, :ungqr!, :unmqr!)
     @eval $f(::ROCSOLVER, args...) = YArocSOLVER.$f(args...)
 end
 
-MatrixAlgebraKit.supports_svd_full(::ROCSOLVER, f::Symbol) = f in (:qr_iteration, :jacobi)
+MatrixAlgebraKit.supports_svd_full(::ROCSOLVER, f::Symbol) = f in (:qr_iteration, :jacobi, :bisection)
 
 function gesvd!(::ROCSOLVER, A::StridedROCMatrix, S::StridedROCVector, U::StridedROCMatrix, Vᴴ::StridedROCMatrix; kwargs...)
     m, n = size(A)
@@ -42,6 +42,12 @@ function gesvdj!(::ROCSOLVER, A::StridedROCMatrix, S::StridedROCVector, U::Strid
     return MatrixAlgebraKit.svd_via_adjoint!(gesvdj!, ROCSOLVER(), A, S, U, Vᴴ; kwargs...)
 end
 
+function gesvdx!(::ROCSOLVER, A::StridedROCMatrix, S::StridedROCVector, U::StridedROCMatrix, Vᴴ::StridedROCMatrix; kwargs...)
+    YArocSOLVER.gesvdx!(A, S, U, Vᴴ; kwargs...)
+    complete_svd_basis!(U, Vᴴ, length(S))
+    return S, U, Vᴴ
+end
+
 heevj!(::ROCSOLVER, A::StridedROCMatrix, Dd::StridedROCVector, V::StridedROCMatrix; kwargs...) =
     YArocSOLVER.heevj!(A, Dd, V; kwargs...)
 heevd!(::ROCSOLVER, A::StridedROCMatrix, Dd::StridedROCVector, V::StridedROCMatrix; kwargs...) =
diff --git a/ext/MatrixAlgebraKitAMDGPUExt/yarocsolver.jl b/ext/MatrixAlgebraKitAMDGPUExt/yarocsolver.jl
index e0c5f084d..28e206660 100644
--- a/ext/MatrixAlgebraKitAMDGPUExt/yarocsolver.jl
+++ b/ext/MatrixAlgebraKitAMDGPUExt/yarocsolver.jl
@@ -175,6 +175,96 @@ for (fname, elty, relty) in
     end
 end
 
+# `gesvdx` computes all singular values, those in the half-open interval `[vl, vu)`, or those
+# with an index in `irange`. Unlike the other algorithms, it never forms the full `U` and `Vᴴ`,
+# so the only job modes are `singular` and `none`.
+function _gesvdx_range(::Type{T}, kwargs) where {T <: Real}
+    if haskey(kwargs, :irange)
+        irange = convert(UnitRange{Int}, kwargs[:irange])
+        return rocSOLVER.rocblas_srange_index, zero(T), zero(T), first(irange), last(irange)
+    elseif haskey(kwargs, :vl) || haskey(kwargs, :vu)
+        vl = convert(T, get(kwargs, :vl, -Inf))
+        vu = convert(T, get(kwargs, :vu, +Inf))
+        return rocSOLVER.rocblas_srange_value, vl, vu, 0, 0
+    else
+        return rocSOLVER.rocblas_srange_all, zero(T), zero(T), 0, 0
+    end
+end
+
+function _gesvdx_jobs(U, Vᴴ, m::Integer, n::Integer, maxnsv::Integer)
+    if length(U) == 0
+        jobu = rocSOLVER.rocblas_svect_none
+    else
+        size(U, 1) == m ||
+            throw(DimensionMismatch("row size mismatch between A ($m) and U ($(size(U, 1)))"))
+        size(U, 2) >= maxnsv ||
+            throw(DimensionMismatch("invalid column size of U"))
+        jobu = rocSOLVER.rocblas_svect_singular
+    end
+    if length(Vᴴ) == 0
+        jobvt = rocSOLVER.rocblas_svect_none
+    else
+        size(Vᴴ, 2) == n ||
+            throw(DimensionMismatch("column size mismatch between A ($n) and Vᴴ ($(size(Vᴴ, 2)))"))
+        size(Vᴴ, 1) >= maxnsv ||
+            throw(DimensionMismatch("invalid row size of Vᴴ"))
+        jobvt = rocSOLVER.rocblas_svect_singular
+    end
+    return jobu, jobvt
+end
+
+# Wrapper for SVD via Bisection
+for (fname, elty, relty) in
+    (
+        (:rocsolver_sgesvdx, :Float32, :Float32),
+        (:rocsolver_dgesvdx, :Float64, :Float64),
+        (:rocsolver_cgesvdx, :ComplexF32, :Float32),
+        (:rocsolver_zgesvdx, :ComplexF64, :Float64),
+    )
+    @eval begin
+        function gesvdx!(
+                A::StridedROCMatrix{$elty},
+                S::StridedROCVector{$relty} = similar(A, $relty, min(size(A)...)),
+                U::StridedROCMatrix{$elty} = similar(A, $elty, size(A, 1), min(size(A)...)),
+                Vᴴ::StridedROCMatrix{$elty} = similar(A, $elty, min(size(A)...), size(A, 2));
+                kwargs...
+            )
+            chkstride1(A, U, Vᴴ, S)
+            m, n = size(A)
+            minmn = min(m, n)
+            srange, vl, vu, il, iu = _gesvdx_range($relty, kwargs)
+            maxnsv = srange == rocSOLVER.rocblas_srange_index ? iu - il + 1 : minmn
+            jobu, jobvt = _gesvdx_jobs(U, Vᴴ, m, n, maxnsv)
+            length(S) == minmn ||
+                throw(DimensionMismatch("length mismatch between A ($minmn) and S ($(length(S)))"))
+
+            lda = max(1, stride(A, 2))
+            ldu = max(1, stride(U, 2))
+            ldv = max(1, stride(Vᴴ, 2))
+            ifail = ROCVector{Cint}(undef, minmn)
+            nsv = ROCVector{Cint}(undef, 1)
+            dh = rocBLAS.handle()
+            dev_info = ROCVector{Cint}(undef, 1)
+            rocSOLVER.$fname(
+                dh, jobu, jobvt, srange, m, n,
+                A, lda, vl, vu, il, iu, nsv,
+                S, U, ldu, Vᴴ, ldv, ifail,
+                dev_info
+            )
+            info = @allowscalar dev_info[1]
+            rocSOLVER.chkargsok(BlasInt(info))
+            # Zero the entries of `S` that `gesvdx` did not write.
+            nv = @allowscalar Int(nsv[1])
+            nv < length(S) && fill!(view(S, (nv + 1):length(S)), zero(eltype(S)))
+
+            AMDGPU.unsafe_free!(nsv)
+            AMDGPU.unsafe_free!(ifail)
+            AMDGPU.unsafe_free!(dev_info)
+            return (S, U, Vᴴ)
+        end
+    end
+end
+
 # for (jname, bname, fname, elty, relty) in
 #     ((:sygvd!, :rocsolverDnSsygvd_bufferSize, :rocsolverDnSsygvd, :Float32, :Float32),
 #      (:sygvd!, :rocsolverDnDsygvd_bufferSize, :rocsolverDnDsygvd, :Float64, :Float64),
diff --git a/src/implementations/svd.jl b/src/implementations/svd.jl
index 3d20e96d4..080019e71 100644
--- a/src/implementations/svd.jl
+++ b/src/implementations/svd.jl
@@ -142,10 +142,16 @@ function svd_via_adjoint!(f!::F, driver::Driver, A, S, U, Vᴴ; kwargs...) where
 end
 
 # LAPACK
-for f! in (:gesdd!, :gesvd!, :gesvdx!, :gesdvd!)
+for f! in (:gesdd!, :gesvd!, :gesdvd!)
     @eval $f!(::LAPACK, args...; kwargs...) = YALAPACK.$f!(args...; kwargs...)
 end
 
+function gesvdx!(::LAPACK, A, S, U, Vᴴ; kwargs...)
+    YALAPACK.gesvdx!(A, S, U, Vᴴ; kwargs...)
+    complete_svd_basis!(U, Vᴴ, length(S))
+    return S, U, Vᴴ
+end
+
 function gesvdj!(::LAPACK, A, S, U, Vᴴ; kwargs...)
     m, n = size(A)
     m >= n && return YALAPACK.gesvdj!(A, S, U, Vᴴ)
@@ -221,7 +227,27 @@ for (f, f_lapack!, Alg) in (
 end
 
 supports_svd_full(::Driver, ::Symbol) = false
-supports_svd_full(::LAPACK, f::Symbol) = f in (:safe_divide_and_conquer, :divide_and_conquer, :qr_iteration)
+supports_svd_full(::LAPACK, f::Symbol) = f in (:safe_divide_and_conquer, :divide_and_conquer, :qr_iteration, :bisection)
+
+# Some methods (e.g. `gesvdx`) only compute the leading `min(m, n)` singular vectors.
+# If `U` or `Vᴴ` is square (`svd_full!`), the remaining columns (row) of
+# `U` (`Vᴴ`) need to be filled with an orthonormal basis for the complement of the
+# computed singular vectors.
+function complete_svd_basis!(U::AbstractMatrix, Vᴴ::AbstractMatrix, minmn::Int)
+    if size(U, 2) > minmn
+        Uc = copy_input(qr_null, view(U, :, 1:minmn))
+        N = view(U, :, (minmn + 1):size(U, 2))
+        N′ = qr_null!(Uc, N)
+        N′ === N || copyto!(N, N′)
+    end
+    if size(Vᴴ, 1) > minmn
+        Vc = copy_input(lq_null, view(Vᴴ, 1:minmn, :))
+        Nᴴ = view(Vᴴ, (minmn + 1):size(Vᴴ, 1), :)
+        Nᴴ′ = lq_null!(Vc, Nᴴ)
+        Nᴴ′ === Nᴴ || copyto!(Nᴴ, Nᴴ′)
+    end
+    return U, Vᴴ
+end
 
 function svd_trunc_no_error!(A, USVᴴ, alg::TruncatedAlgorithm)
     U, S, Vᴴ = svd_compact!(A, USVᴴ, alg.alg)
diff --git a/src/yalapack.jl b/src/yalapack.jl
index 57e974bda..f6ca7a507 100644
--- a/src/yalapack.jl
+++ b/src/yalapack.jl
@@ -2235,8 +2235,11 @@ for (gesvd, gesdd, gesvdx, gejsv, gesvj, elty, relty) in
             else
                 size(U, 1) == m ||
                     throw(DimensionMismatch("row size mismatch between A ($m) and U ($(size(U, 1)))"))
-                size(U, 2) >= (range == 'I' ? iu - il + 1 : minmn) ||
-                    throw(DimensionMismatch("invalid column size of U"))
+                if range == 'I'
+                    (size(U, 2) >= iu - il + 1 && size(U, 2) <= m) || throw(DimensionMismatch("invalid column size of U"))
+                else
+                    (size(U, 2) == minmn || size(U, 2) == m) || throw(DimensionMismatch("invalid column size of U"))
+                end
                 jobu = 'V'
             end
             if length(Vᴴ) == 0
@@ -2244,8 +2247,11 @@ for (gesvd, gesdd, gesvdx, gejsv, gesvj, elty, relty) in
             else
                 size(Vᴴ, 2) == n ||
                     throw(DimensionMismatch("column size mismatch between A ($n) and Vᴴ ($(size(Vᴴ, 2)))"))
-                size(Vᴴ, 1) >= (range == 'I' ? iu - il + 1 : minmn) ||
-                    throw(DimensionMismatch("invalid row size of Vᴴ"))
+                if range == 'I'
+                    (size(Vᴴ, 1) >= iu - il + 1 && size(Vᴴ, 1) <= n) || throw(DimensionMismatch("invalid row size of Vᴴ"))
+                else
+                    (size(Vᴴ, 1) == minmn || size(Vᴴ, 1) == n) || throw(DimensionMismatch("invalid row size of Vᴴ"))
+                end
                 jobvt = 'V'
             end
             length(S) == minmn ||
diff --git a/test/decompositions/svd.jl b/test/decompositions/svd.jl
index c69ed3a0e..5387252a3 100644
--- a/test/decompositions/svd.jl
+++ b/test/decompositions/svd.jl
@@ -21,7 +21,7 @@ if !is_buildkite
     # LAPACK algorithms:
     for T in BLASFloats, m in (0, 54), n in (0, 37, m, 63)
         TestSuite.seed_rng!(123)
-        LAPACK_SVD_ALGS = (QRIteration(), DivideAndConquer(), SafeDivideAndConquer(; fixgauge = true))
+        LAPACK_SVD_ALGS = (QRIteration(), DivideAndConquer(), SafeDivideAndConquer(; fixgauge = true), Bisection())
         TestSuite.test_svd(T, (m, n))
         TestSuite.test_svd_algs(T, (m, n), LAPACK_SVD_ALGS)
         @static if VERSION > v"1.11-" # Jacobi broken on 1.10
@@ -81,7 +81,7 @@ if AMDGPU.functional()
     for T in BLASFloats, m in (0, 23), n in (0, 17, m, 27)
         TestSuite.seed_rng!(123)
         TestSuite.test_svd(ROCMatrix{T}, (m, n))
-        AMD_SVD_ALGS = (QRIteration(), Jacobi())
+        AMD_SVD_ALGS = (QRIteration(), Jacobi(), Bisection())
         TestSuite.test_svd_algs(ROCMatrix{T}, (m, n), AMD_SVD_ALGS)
     end