diff --git a/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl b/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl
index 2d722fe77..7e2a44fd0 100644
--- a/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl
+++ b/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl
@@ -20,13 +20,13 @@ MatrixAlgebraKit.default_driver(::Type{TA}) where {TA <: StridedROCArray{<:BlasF
 MatrixAlgebraKit.default_driver(::Type{TA}) where {TA <: AbstractVector{<:StridedROCMatrix{<:BlasFloat}}} = ROCSOLVER()
 
 function MatrixAlgebraKit.default_svd_algorithm(::Type{T}; kwargs...) where {T <: StridedROCMatrix{<:BlasFloat}}
-    return QRIteration(; kwargs...)
+    return Bisection(; kwargs...)
 end
 function MatrixAlgebraKit.default_svd_algorithm(::Type{T}; kwargs...) where {T <: StridedROCArray{<:BlasFloat, 3}}
-    return QRIteration(; kwargs...)
+    return Bisection(; kwargs...)
 end
 function MatrixAlgebraKit.default_svd_algorithm(::Type{T}; kwargs...) where {T <: AbstractVector{<:StridedROCMatrix{<:BlasFloat}}}
-    return QRIteration(; kwargs...)
+    return Bisection(; kwargs...)
 end
 function MatrixAlgebraKit.default_eigh_algorithm(::Type{T}; kwargs...) where {T <: StridedROCVecOrMat{<:BlasFloat}}
     return DivideAndConquer(; kwargs...)
@@ -55,8 +55,14 @@ function gesvdj!(::ROCSOLVER, A::StridedROCMatrix, S::StridedROCVector, U::Strid
     return MatrixAlgebraKit.svd_via_adjoint!(gesvdj!, ROCSOLVER(), A, S, U, Vᴴ; kwargs...)
 end
 
-gesvdx!(::ROCSOLVER, A::StridedROCMatrix, S::StridedROCVector, U::StridedROCMatrix, Vᴴ::StridedROCMatrix; kwargs...) =
-    YArocSOLVER.gesvdx!(A, S, U, Vᴴ; kwargs...)
+function gesvdx!(::ROCSOLVER, A::StridedROCMatrix, S::StridedROCVector, U::StridedROCMatrix, Vᴴ::StridedROCMatrix; kwargs...)
+    if min(size(A)...) == 1
+        _gesvdx_rank1!(A, S, U, Vᴴ; kwargs...)
+    else
+        YArocSOLVER.gesvdx!(A, S, U, Vᴴ; kwargs...)
+    end
+    return S, U, Vᴴ
+end
 
 # rocSOLVER's batched `gesvd` requires m ≥ n, so wide matrices go through the adjoint
 function gesvd_batched!(::ROCSOLVER, As::AbstractVector{<:StridedROCMatrix}, Ss::StridedROCMatrix, Us::StridedROCArray{T, 3}, Vᴴs::StridedROCArray{T, 3}; kwargs...) where {T <: BlasFloat}
@@ -80,14 +86,64 @@ gesvdj_batched!(::ROCSOLVER, As::AbstractVector{<:StridedROCMatrix}, Ss::Strided
 gesvdj_batched!(::ROCSOLVER, As::StridedROCArray{T, 3}, Ss::StridedROCMatrix, Us::StridedROCArray{T, 3}, Vᴴs::StridedROCArray{T, 3}; kwargs...) where {T <: BlasFloat} =
     YArocSOLVER.gesvdj_strided_batched!(As, Ss, Us, Vᴴs; kwargs...)
 
-gesvdx_batched!(::ROCSOLVER, As::AbstractVector{<:StridedROCMatrix}, Ss::StridedROCMatrix, Us::StridedROCArray{T, 3}, Vᴴs::StridedROCArray{T, 3}; kwargs...) where {T <: BlasFloat} =
-    YArocSOLVER.gesvdx_batched!(As, Ss, Us, Vᴴs; kwargs...)
-gesvdx_batched!(::ROCSOLVER, As::StridedROCArray{T, 3}, Ss::StridedROCMatrix, Us::StridedROCArray{T, 3}, Vᴴs::StridedROCArray{T, 3}; kwargs...) where {T <: BlasFloat} =
-    YArocSOLVER.gesvdx_strided_batched!(As, Ss, Us, Vᴴs; kwargs...)
+function gesvdx_batched!(::ROCSOLVER, As::AbstractVector{<:StridedROCMatrix}, Ss::StridedROCMatrix, Us::StridedROCArray{T, 3}, Vᴴs::StridedROCArray{T, 3}; kwargs...) where {T <: BlasFloat}
+    if min(size(first(As))...) == 1
+        _gesvdx_rank1_batched!(As, Ss, Us, Vᴴs; kwargs...)
+    else
+        YArocSOLVER.gesvdx_batched!(As, Ss, Us, Vᴴs; kwargs...)
+    end
+    return Ss, Us, Vᴴs
+end
+function gesvdx_batched!(::ROCSOLVER, As::StridedROCArray{T, 3}, Ss::StridedROCMatrix, Us::StridedROCArray{T, 3}, Vᴴs::StridedROCArray{T, 3}; kwargs...) where {T <: BlasFloat}
+    if min(size(As, 1), size(As, 2)) == 1
+        _gesvdx_rank1_batched!(As, Ss, Us, Vᴴs; kwargs...)
+    else
+        YArocSOLVER.gesvdx_strided_batched!(As, Ss, Us, Vᴴs; kwargs...)
+    end
+    return Ss, Us, Vᴴs
+end
 
 gesdd!(::ROCSOLVER, A::StridedROCMatrix, S::StridedROCVector, U::StridedROCMatrix, Vᴴ::StridedROCMatrix; kwargs...) =
     YArocSOLVER.gesdd!(A, S, U, Vᴴ; kwargs...)
 
+function _gesvdx_rank1!(A::StridedROCMatrix, S::StridedROCVector, U::StridedROCMatrix, Vᴴ::StridedROCMatrix; kwargs...)
+    select_kwargs = Base.structdiff(NamedTuple(kwargs), (; irange = nothing, vl = nothing, vu = nothing))
+    nrmA = norm(A)
+    fill!(S, nrmA)
+    if !isempty(U) && !isempty(Vᴴ)
+        u, v = view(U, :, 1), view(Vᴴ, 1, :)
+        x, e = size(A, 1) == 1 ? (v, u) : (u, v)
+        if iszero(nrmA)
+            zero!(x)
+            fill!(view(x, 1:1), one(eltype(x)))
+        else
+            copyto!(x, vec(A))
+            x ./= nrmA
+        end
+        fill!(e, one(eltype(e)))
+    end
+    _gesvdx_apply_range!(S, select_kwargs)
+    return S, U, Vᴴ
+end
+
+function _gesvdx_rank1_batched!(As, Ss::StridedROCMatrix, Us, Vᴴs; kwargs...)
+    select_kwargs = Base.structdiff(NamedTuple(kwargs), (; irange = nothing, vl = nothing, vu = nothing))
+    gesvdj_batched!(ROCSOLVER(), As, Ss, Us, Vᴴs; select_kwargs...)
+    _gesvdx_apply_range!(Ss, select_kwargs)
+    return Ss, Us, Vᴴs
+end
+
+function _gesvdx_apply_range!(S, select::NamedTuple)
+    if haskey(select, :irange)
+        1 in convert(UnitRange{Int}, select.irange) || zero!(S)
+    elseif haskey(select, :vl) || haskey(select, :vu)
+        vl = convert(eltype(S), get(select, :vl, -Inf))
+        vu = convert(eltype(S), get(select, :vu, Inf))
+        S .= ifelse.((vl .<= S) .& (S .< vu), S, zero(eltype(S)))
+    end
+    return S
+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/test/decompositions/svd.jl b/test/decompositions/svd.jl
index 9d9288ddb..a0faf4343 100644
--- a/test/decompositions/svd.jl
+++ b/test/decompositions/svd.jl
@@ -1,5 +1,6 @@
 using MatrixAlgebraKit
-using LinearAlgebra: Diagonal
+using Test
+using LinearAlgebra: Diagonal, isposdef
 using CUDA, AMDGPU
 
 if @isdefined(fast_tests) && fast_tests
@@ -12,6 +13,7 @@ end
 
 @isdefined(TestSuite) || include("../testsuite/TestSuite.jl")
 using .TestSuite
+using .TestSuite: testargs_summary
 
 is_buildkite = get(ENV, "BUILDKITE", "false") == "true"
 
@@ -88,7 +90,7 @@ end
 # ------------
 if AMDGPU.functional()
     # ROCSOLVER algorithms:
-    for T in BLASFloats, m in (0, 23), n in (0, 17, m, 27)
+    for T in BLASFloats, m in (0, 1, 23), n in (0, 1, 17, m, 27)
         TestSuite.seed_rng!(123)
         TestSuite.test_svd(ROCMatrix{T}, (m, n))
         AMD_SVD_ALGS = (QRIteration(), Jacobi(), DivideAndConquer(), Bisection())
@@ -97,6 +99,21 @@ if AMDGPU.functional()
         TestSuite.test_svd_batched_algs(ROCMatrix{T}, (m, n), batch_size, AMD_SVD_ALGS)
     end
 
+    @testset "Bisection with min(m, n) == 1 $(testargs_summary(T, sz))" for T in BLASFloats,
+            sz in ((1, 1), (2, 1), (5, 1), (1, 2), (1, 5))
+
+        TestSuite.seed_rng!(123)
+        for _ in 1:16
+            A = TestSuite.instantiate_matrix(ROCMatrix{T}, sz)
+            U, S, Vᴴ = svd_compact(A; alg = Bisection())
+            @test U * S * Vᴴ ≈ A
+            @test isisometric(U)
+            @test isisometric(Vᴴ; side = :right)
+            @test isposdef(S)
+            @test Array(S) ≈ Diagonal(svd_vals(Array(A)))
+        end
+    end
+
     # Diagonal:
     for T in BLASFloats, m in (0, 23)
         TestSuite.seed_rng!(123)
diff --git a/test/testsuite/decompositions/svd.jl b/test/testsuite/decompositions/svd.jl
index a0fddda61..914f28054 100644
--- a/test/testsuite/decompositions/svd.jl
+++ b/test/testsuite/decompositions/svd.jl
@@ -468,7 +468,7 @@ function test_svd_trunc(
         S₀ = collect(svd_vals(A))
         r = minmn - 2
 
-        if m > 0 && n > 0
+        if m > 0 && n > 0 && r >= 0
             U1, S1, V1ᴴ, ϵ1 = @testinferred svd_trunc(A; trunc = truncrank(r))
             @test length(diagview(S1)) == r
             @test collect(diagview(S1)) ≈ S₀[1:r]
@@ -573,7 +573,7 @@ function test_svd_trunc_algs(
         S₀ = collect(svd_vals(A))
         r = minmn - 2
 
-        if m > 0 && n > 0
+        if m > 0 && n > 0 && r >= 0
             U1, S1, V1ᴴ, ϵ1 = @testinferred svd_trunc(A; trunc = truncrank(r), alg)
             @test length(diagview(S1)) == r
             @test collect(diagview(S1)) ≈ S₀[1:r]