diff --git a/scipy/sparse/linalg/_isolve/tests/test_iterative.py b/scipy/sparse/linalg/_isolve/tests/test_iterative.py

index a782a8d27c2..48fc16b7a00 100644

--- a/scipy/sparse/linalg/_isolve/tests/test_iterative.py

+++ b/scipy/sparse/linalg/_isolve/tests/test_iterative.py

@@ -409,7 +409,9 @@ def test_atol(solver):

         residual = A.dot(x) - b

         err = np.linalg.norm(residual)

         atol2 = tol * b_norm

-        assert_(err <= max(atol, atol2))

+        # Added 1.00025 fudge factor because of `err` exceeding `atol` just

+        # very slightly on s390x (see gh-17839)

+        assert_(err <= 1.00025 * max(atol, atol2))

 @pytest.mark.parametrize("solver", [cg, cgs, bicg, bicgstab, gmres, qmr, minres, lgmres, gcrotmk, tfqmr])

@@ -452,8 +454,10 @@ def test_zero_rhs(solver):

                                                 and sys.version_info[1] == 9,

                                                 reason="gh-13019")),

     qmr,

-    pytest.param(lgmres, marks=pytest.mark.xfail(platform.machine() == 'ppc64le',

-                                                 reason="fails on ppc64le")),

+    pytest.param(lgmres, marks=pytest.mark.xfail(

+        platform.machine() not in ['x86_64' 'x86', 'aarch64', 'arm64'],

+        reason="fails on at least ppc64le, ppc64 and riscv64, see gh-17839")

+    ),

     pytest.param(cgs, marks=pytest.mark.xfail),

     pytest.param(bicg, marks=pytest.mark.xfail),

     pytest.param(bicgstab, marks=pytest.mark.xfail),

diff --git a/scipy/special/tests/test_orthogonal.py b/scipy/special/tests/test_orthogonal.py

index a325cb1a9ef..408b03bde2e 100644

--- a/scipy/special/tests/test_orthogonal.py

+++ b/scipy/special/tests/test_orthogonal.py

@@ -546,7 +546,7 @@ def test_roots_gegenbauer():

     vgq(rootf(170), evalf(170), weightf(170), -1., 1., 5, atol=1e-13)

     vgq(rootf(170), evalf(170), weightf(170), -1., 1., 25, atol=1e-12)

     vgq(rootf(170), evalf(170), weightf(170), -1., 1., 100, atol=1e-11)

-    vgq(rootf(170.5), evalf(170.5), weightf(170.5), -1., 1., 5, atol=1e-13)

+    vgq(rootf(170.5), evalf(170.5), weightf(170.5), -1., 1., 5, atol=1.25e-13)

     vgq(rootf(170.5), evalf(170.5), weightf(170.5), -1., 1., 25, atol=1e-12)

     vgq(rootf(170.5), evalf(170.5), weightf(170.5), -1., 1., 100, atol=1e-11)

diff --git a/scipy/stats/tests/test_distributions.py b/scipy/stats/tests/test_distributions.py

index eceeafdffe0..139b0537174 100644

--- a/scipy/stats/tests/test_distributions.py

+++ b/scipy/stats/tests/test_distributions.py

@@ -4254,7 +4254,7 @@ def test_pdf_nolan_samples(

             ],

             # for small alpha very slightly reduced accuracy

             [

-                'piecewise', 5e-11, lambda r: (

+                'piecewise', 2.5e-10, lambda r: (

                     np.isin(r['pct'], pct_range) &

                     np.isin(r['alpha'], alpha_range) &

                     np.isin(r['beta'], beta_range) &

@@ -4358,7 +4358,7 @@ def test_cdf_nolan_samples(

         tests = [

             # piecewise generally good accuracy

             [

-                'piecewise', 1e-12, lambda r: (

+                'piecewise', 2e-12, lambda r: (

                     np.isin(r['pct'], pct_range) &

                     np.isin(r['alpha'], alpha_range) &

                     np.isin(r['beta'], beta_range) &

@@ -4480,6 +4480,14 @@ def test_location_scale(

     ):

         """Tests for pdf and cdf where loc, scale are different from 0, 1

         """

+

+        uname = platform.uname()

+        is_linux_32 = uname.system == 'Linux' and "32bit" in platform.architecture()[0]

+        # Test seems to be unstable (see gh-17839 for a bug report on Debian

+        # i386), so skip it.

+        if is_linux_32 and case == 'pdf':

+            pytest.skip("Test unstable on some platforms; see gh-17839, 17859")

+

         data = nolan_loc_scale_sample_data

         # We only test against piecewise as location/scale transforms

         # are same for other methods.

diff --git a/scipy/stats/tests/test_mstats_basic.py b/scipy/stats/tests/test_mstats_basic.py

index cd53c7b7914..76cbfd8c253 100644

--- a/scipy/stats/tests/test_mstats_basic.py

+++ b/scipy/stats/tests/test_mstats_basic.py

@@ -1768,8 +1768,8 @@ def test_skewtest_2D_WithMask(self):

                 r = stats.skewtest(x)

                 rm = stats.mstats.skewtest(xm)

-                assert_allclose(r[0][0], rm[0][0], rtol=2e-15)

-                assert_allclose(r[0][1], rm[0][1], rtol=1e-15)

+                assert_allclose(r[0][0], rm[0][0], rtol=1e-14)

+                assert_allclose(r[0][1], rm[0][1], rtol=1e-14)

     def test_normaltest(self):

         with np.errstate(over='raise'), suppress_warnings() as sup: