diff --git a/Eigen/Eigenvalues b/Eigen/Eigenvalues
index c11f42ad4..803900058 100644
--- a/Eigen/Eigenvalues
+++ b/Eigen/Eigenvalues
@@ -15,6 +15,7 @@
 #include "Householder"
 #include "LU"
 #include "Geometry"
+#include "Sparse"  // Needed by ComplexQZ.
 
 #include "src/Core/util/DisableStupidWarnings.h"
 
diff --git a/Eigen/src/Core/arch/AVX/PacketMath.h b/Eigen/src/Core/arch/AVX/PacketMath.h
index 0cd9e6cd6..b1dfb07ff 100644
--- a/Eigen/src/Core/arch/AVX/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX/PacketMath.h
@@ -2831,7 +2831,7 @@ inline __m128i segment_mask_4x8(Index begin, Index count) {
   mask <<= CHAR_BIT * count;
   mask--;
   mask <<= CHAR_BIT * begin;
-#if defined(_WIN32) && !defined(_WIN64)
+#if !EIGEN_ARCH_x86_64
   return _mm_loadl_epi64(reinterpret_cast<const __m128i*>(&mask));
 #else
   return _mm_cvtsi64_si128(mask);
@@ -2847,7 +2847,7 @@ inline __m128i segment_mask_8x8(Index begin, Index count) {
   mask <<= (CHAR_BIT / 2) * count;
   mask--;
   mask <<= CHAR_BIT * begin;
-#if defined(_WIN32) && !defined(_WIN64)
+#if !EIGEN_ARCH_x86_64
   return _mm_loadl_epi64(reinterpret_cast<const __m128i*>(&mask));
 #else
   return _mm_cvtsi64_si128(mask);
diff --git a/Eigen/src/Eigenvalues/ComplexQZ.h b/Eigen/src/Eigenvalues/ComplexQZ.h
index 20f2a77bb..ed32ea3da 100644
--- a/Eigen/src/Eigenvalues/ComplexQZ.h
+++ b/Eigen/src/Eigenvalues/ComplexQZ.h
@@ -14,8 +14,6 @@
 #ifndef EIGEN_COMPLEX_QZ_H_
 #define EIGEN_COMPLEX_QZ_H_
 
-#include "../../Sparse"
-
 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"
 
@@ -126,9 +124,7 @@ class ComplexQZ {
             computeQZ ? n : (MatrixType::ColsAtCompileTime == Eigen::Dynamic ? 0 : MatrixType::ColsAtCompileTime)),
         m_ws(2 * n),
         m_computeQZ(computeQZ),
-        m_maxIters(maxIters){
-
-        };
+        m_maxIters(maxIters) {}
 
   /** \brief Constructor. computes the QZ decomposition of given matrices
    * upon creation
@@ -178,14 +174,14 @@ class ComplexQZ {
    *
    * \returns \c Success if computation was successfull, \c NoConvergence otherwise.
    */
-  ComputationInfo info() const { return m_info; };
+  ComputationInfo info() const { return m_info; }
 
   /** \brief number of performed QZ steps
    */
   unsigned int iterations() const {
     eigen_assert(m_isInitialized && "ComplexQZ is not initialized.");
     return m_global_iter;
-  };
+  }
 
  private:
   Index m_n;
@@ -569,7 +565,9 @@ void ComplexQZ<MatrixType_>::push_down_zero_ST(Index k, Index l) {
   for (Index j = k + 1; j <= l; j++) {
     // Create a 0 at _T(j, j)
     J.makeGivens(m_T(j - 1, j), m_T(j, j), &m_T.coeffRef(j - 1, j));
-    m_T.rightCols(m_n - j - 1).applyOnTheLeft(j - 1, j, J.adjoint());
+    if (m_n - j - 1 > 0) {
+      m_T.rightCols(m_n - j - 1).applyOnTheLeft(j - 1, j, J.adjoint());
+    }
     m_T.coeffRef(j, j) = Scalar(0);
 
     m_S.applyOnTheLeft(j - 1, j, J.adjoint());
diff --git a/Eigen/src/Householder/Householder.h b/Eigen/src/Householder/Householder.h
index 96b1daf5f..e5d2d4fac 100644
--- a/Eigen/src/Householder/Householder.h
+++ b/Eigen/src/Householder/Householder.h
@@ -65,7 +65,6 @@ template <typename EssentialPart>
 EIGEN_DEVICE_FUNC void MatrixBase<Derived>::makeHouseholder(EssentialPart& essential, Scalar& tau,
                                                             RealScalar& beta) const {
   using numext::conj;
-  using numext::sqrt;
 
   EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
   VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size() - 1);
@@ -79,7 +78,7 @@ EIGEN_DEVICE_FUNC void MatrixBase<Derived>::makeHouseholder(EssentialPart& essen
     beta = numext::real(c0);
     essential.setZero();
   } else {
-    beta = sqrt(numext::abs2(c0) + tailSqNorm);
+    beta = numext::sqrt(numext::abs2(c0) + tailSqNorm);
     if (numext::real(c0) >= RealScalar(0)) beta = -beta;
     essential = tail / (c0 - beta);
     tau = conj((beta - c0) / beta);
diff --git a/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h b/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h
index 3c65541b8..97f214201 100644
--- a/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h
+++ b/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h
@@ -89,7 +89,7 @@ struct simpl_chol_helper {
         m_set[u] = v;
         u = next;
       }
-    };
+    }
   };
 
   // Computes the higher adjacency pattern by transposing the input lower adjacency matrix.
diff --git a/Eigen/src/SparseCore/SparseVector.h b/Eigen/src/SparseCore/SparseVector.h
index d19a00dd9..c8d34e318 100644
--- a/Eigen/src/SparseCore/SparseVector.h
+++ b/Eigen/src/SparseCore/SparseVector.h
@@ -140,7 +140,7 @@ class SparseVector : public SparseCompressedBase<SparseVector<Scalar_, Options_,
     return insertBack(inner);
   }
   inline Scalar& insertBack(Index i) {
-    m_data.append(0, i);
+    m_data.append(Scalar(0), i);
     return m_data.value(m_data.size() - 1);
   }
 
@@ -150,7 +150,7 @@ class SparseVector : public SparseCompressedBase<SparseVector<Scalar_, Options_,
     return insertBackUnordered(inner);
   }
   inline Scalar& insertBackUnordered(Index i) {
-    m_data.append(0, i);
+    m_data.append(Scalar(0), i);
     return m_data.value(m_data.size() - 1);
   }
 
@@ -177,7 +177,7 @@ class SparseVector : public SparseCompressedBase<SparseVector<Scalar_, Options_,
       --p;
     }
     m_data.index(p + 1) = convert_index(i);
-    m_data.value(p + 1) = 0;
+    m_data.value(p + 1) = Scalar(0);
     return m_data.value(p + 1);
   }
 
@@ -367,7 +367,7 @@ class SparseVector : public SparseCompressedBase<SparseVector<Scalar_, Options_,
 
   /** \internal \deprecated use insertBack(Index) */
   EIGEN_DEPRECATED_WITH_REASON("Use .insertBack() instead.") Scalar& fill(Index i) {
-    m_data.append(0, i);
+    m_data.append(Scalar(0), i);
     return m_data.value(m_data.size() - 1);
   }
 
diff --git a/ci/build.linux.gitlab-ci.yml b/ci/build.linux.gitlab-ci.yml
index 2fb7aa115..9e6303488 100644
--- a/ci/build.linux.gitlab-ci.yml
+++ b/ci/build.linux.gitlab-ci.yml
@@ -290,7 +290,7 @@ build:linux:cross:x86-64:gcc-10:default:smoketest:
   rules:
     - if: $CI_PIPELINE_SOURCE == "merge_request_event"
   tags:
-    - saas-linux-small-amd64
+    - saas-linux-medium-amd64
 
 build:linux:cross:x86-64:clang-12:default:smoketest:
   extends: build:linux:cross:x86-64:clang-12:default
@@ -299,4 +299,4 @@ build:linux:cross:x86-64:clang-12:default:smoketest:
   rules:
     - if: $CI_PIPELINE_SOURCE == "merge_request_event"
   tags:
-    - saas-linux-small-amd64
+    - saas-linux-medium-amd64
diff --git a/ci/scripts/test.linux.script.sh b/ci/scripts/test.linux.script.sh
index 0bd18a859..6e2e1c58c 100755
--- a/ci/scripts/test.linux.script.sh
+++ b/ci/scripts/test.linux.script.sh
@@ -13,19 +13,29 @@ elif [[ ${EIGEN_CI_CTEST_LABEL} ]]; then
   target="-L ${EIGEN_CI_CTEST_LABEL}"
 fi
 
-# Repeat tests up to three times to ignore flakes.  Do not re-run with -T test,
-# otherwise we lose test results for those that passed.
-# Note: starting with CMake 3.17, we can use --repeat until-pass:3, but we have
-#       no way of easily installing this on ppc64le.
-ctest ${EIGEN_CI_CTEST_ARGS} --parallel ${NPROC} \
-      --output-on-failure --no-compress-output  \
-      --build-no-clean -T test ${target} || \
-  ctest ${EIGEN_CI_CTEST_ARGS} --parallel ${NPROC} \
-      --output-on-failure --no-compress-output --rerun-failed || \
-  ctest ${EIGEN_CI_CTEST_ARGS} --parallel ${NPROC} \
-      --output-on-failure --no-compress-output --rerun-failed
+set +x
+
+ctest_cmd="ctest ${EIGEN_CI_CTEST_ARGS} --parallel ${NPROC} --output-on-failure --no-compress-output --build-noclean ${target}"
+
+echo "Running initial tests..."
+if ${ctest_cmd} -T test; then
+  echo "Tests passed on the first attempt."
+  exit_code=$?
+else
+  echo "Initial tests failed with exit code $?. Retrying up to ${EIGEN_CI_CTEST_REPEAT} times..."
+  if ${ctest_cmd} --rerun-failed --repeat until-pass:${EIGEN_CI_CTEST_REPEAT}; then
+    echo "Tests passed on retry."
+    exit_code=42
+  else
+    exit_code=$?
+  fi
+fi
+
+set -x
 
 # Return to root directory.
 cd ${rootdir}
 
 set +x
+
+exit $exit_code
diff --git a/ci/scripts/test.windows.script.ps1 b/ci/scripts/test.windows.script.ps1
index 4ea1e30f5..ba46ef1cc 100644
--- a/ci/scripts/test.windows.script.ps1
+++ b/ci/scripts/test.windows.script.ps1
@@ -13,18 +13,32 @@ if (${EIGEN_CI_CTEST_REGEX}) {
   $target = "-L","${EIGEN_CI_CTEST_LABEL}"
 }
 
-# Repeat tests up to three times to ignore flakes.  Do not re-run with -T test,
-# otherwise we lose test results for those that passed.
-# Note: starting with CMake 3.17, we can use --repeat until-pass:3, but we have
-#       no way of easily installing this on ppc64le.
-ctest $EIGEN_CI_CTEST_ARGS -j$NPROC --output-on-failure --no-compress-output --build-no-clean -T test $target || `
-  ctest $EIGEN_CI_CTEST_ARGS -j$NPROC --output-on-failure --no-compress-output --rerun-failed || `
-  ctest $EIGEN_CI_CTEST_ARGS -j$NPROC --output-on-failure --no-compress-output --rerun-failed
+$ctest_cmd = { ctest ${EIGEN_CI_CTEST_ARGS} --parallel ${NPROC} --output-on-failure --no-compress-output --build-noclean ${target} }
 
-$success = $LASTEXITCODE
+Write-Host "Running initial tests..."
+
+& $ctest_cmd "-T test"
+$exit_code = $LASTEXITCODE
+
+if ($exit_code -eq 0) {
+  Write-Host "Tests passed on the first attempt."
+}
+else {
+  Write-Host "Initial tests failed with exit code $exit_code. Retrying up to $EIGEN_CI_CTEST_REPEAT times..."
+  # TODO: figure out how to use --repeat until-pass
+  for ($i = 1; $i -le $EIGEN_CI_CTEST_REPEAT; $i++) {
+    & $ctest_cmd "--rerun-failed"
+    $exit_code = $LASTEXITCODE
+
+    if ($exit_code -eq 0) {
+      Write-Host "Tests passed on retry."
+      $exit_code = 42
+      break
+    }
+  }
+}
 
 # Return to root directory.
 cd ${rootdir}
 
-# Explicitly propagate exit code to indicate pass/failure of test command.
-if($success -ne 0) { Exit $success }
+Exit $exit_code
diff --git a/ci/test.linux.gitlab-ci.yml b/ci/test.linux.gitlab-ci.yml
index b3599f38f..17c7ee0e2 100644
--- a/ci/test.linux.gitlab-ci.yml
+++ b/ci/test.linux.gitlab-ci.yml
@@ -11,6 +11,8 @@
     - if: $CI_PIPELINE_SOURCE == "merge_request_event" && $CI_PROJECT_NAMESPACE == "libeigen" && $CI_MERGE_REQUEST_LABELS =~ "/all-tests/"
   tags:
     - saas-linux-2xlarge-amd64
+  allow_failure:
+    exit_codes: 42
 
 ##### x86-64 ###################################################################
 .test:linux:x86-64:
@@ -384,7 +386,7 @@ test:linux:x86-64:gcc-10:default:smoketest:
   rules:
     - if: $CI_PIPELINE_SOURCE == "merge_request_event"
   tags:
-    - saas-linux-small-amd64
+    - saas-linux-medium-amd64
 
 test:linux:x86-64:clang-12:default:smoketest:
   extends: .test:linux:x86-64:clang-12:default
@@ -394,4 +396,4 @@ test:linux:x86-64:clang-12:default:smoketest:
   rules:
     - if: $CI_PIPELINE_SOURCE == "merge_request_event"
   tags:
-    - saas-linux-small-amd64
+    - saas-linux-medium-amd64
diff --git a/ci/test.windows.gitlab-ci.yml b/ci/test.windows.gitlab-ci.yml
index 3c398a4ec..34b1d7424 100644
--- a/ci/test.windows.gitlab-ci.yml
+++ b/ci/test.windows.gitlab-ci.yml
@@ -9,11 +9,12 @@
     - if: $CI_PIPELINE_SOURCE == "schedule" && $CI_PROJECT_NAMESPACE == "libeigen"
     - if: $CI_PIPELINE_SOURCE == "web" && $CI_PROJECT_NAMESPACE == "libeigen"
     - if: $CI_PIPELINE_SOURCE == "merge_request_event" && $CI_PROJECT_NAMESPACE == "libeigen" && $CI_MERGE_REQUEST_LABELS =~ "/all-tests/"
-
   tags:
     - eigen-runner
     - windows
     - x86-64
+  allow_failure:
+    exit_codes: 42
 
 ##### MSVC #####################################################################
 
diff --git a/cmake/EigenSmokeTestList.cmake b/cmake/EigenSmokeTestList.cmake
index db7d3ff5e..247b2c4a2 100644
--- a/cmake/EigenSmokeTestList.cmake
+++ b/cmake/EigenSmokeTestList.cmake
@@ -91,7 +91,7 @@ set(ei_smoke_test_list
   qr_1
   qr_colpivoting_7
   qr_fullpivoting_4
-  rand
+  rand_1
   real_qz_1
   redux_1
   ref_1
diff --git a/doc/TopicCMakeGuide.dox b/doc/TopicCMakeGuide.dox
index ebbc4a840..dc0d7068c 100644
--- a/doc/TopicCMakeGuide.dox
+++ b/doc/TopicCMakeGuide.dox
@@ -36,9 +36,9 @@ option in `find_package`:
 ```
 find_package(Eigen3 3.4 REQUIRED NO_MODULE)  # Restricts to 3.4.z
 ```
-or to support a range of versions:
+Starting with Eigen 3.4.1, we also support a range spanning major versions:
 ```
-find_package(Eigen3 3.4...5 REQUIRED NO_MODULE)  # Any version >=3.4.0 but <6.0.0.
+find_package(Eigen3 3.4...5 REQUIRED NO_MODULE)  # Any version >=3.4.1 but <6.0.0.
 ```
 
 Do not forget to set the <a href="https://cmake.org/cmake/help/v3.7/variable/CMAKE_PREFIX_PATH.html">\c CMAKE_PREFIX_PATH </a> variable if Eigen is not installed in a default location or if you want to pick a specific version. For instance:
diff --git a/test/complex_qz.cpp b/test/complex_qz.cpp
index a6b05dc92..28ab08e93 100644
--- a/test/complex_qz.cpp
+++ b/test/complex_qz.cpp
@@ -18,11 +18,9 @@
 
 template <typename MatrixType>
 void generate_random_matrix_pair(const Index dim, MatrixType& A, MatrixType& B) {
-  A.resize(dim, dim);
-  B.resize(dim, dim);
-  A.setRandom();
-  B.setRandom();
-  // Set each row of B with a probability of 10% to 0
+  A.setRandom(dim, dim);
+  B.setRandom(dim, dim);
+  // Zero out each row of B to with a probability of 10%.
   for (int i = 0; i < dim; i++) {
     if (internal::random<int>(0, 10) == 0) B.row(i).setZero();
   }
@@ -59,8 +57,6 @@ void complex_qz(const MatrixType& A, const MatrixType& B) {
 }
 
 EIGEN_DECLARE_TEST(complex_qz) {
-  // const Index dim1 = 15;
-  // const Index dim2 = 80;
   for (int i = 0; i < g_repeat; i++) {
     // Check for very small, fixed-sized double- and float complex matrices
     Eigen::Matrix2cd A_2x2, B_2x2;
@@ -71,16 +67,18 @@ EIGEN_DECLARE_TEST(complex_qz) {
     A_3x3.setRandom();
     B_3x3.setRandom();
     B_3x3.col(i % 3).setRandom();
-    // Test for small float complex matrices
-    Eigen::MatrixXcf A_float, B_float;
-    const Index dim1 = internal::random<Index>(15, 80), dim2 = internal::random<Index>(15, 80);
-    generate_random_matrix_pair(dim1, A_float, B_float);
-    // Test for a bit larger double complex matrices
-    Eigen::MatrixXcd A_double, B_double;
-    generate_random_matrix_pair(dim2, A_double, B_double);
     CALL_SUBTEST_1(complex_qz(A_2x2, B_2x2));
     CALL_SUBTEST_2(complex_qz(A_3x3, B_3x3));
+
+    // Test for float complex matrices
+    const Index dim = internal::random<Index>(15, 80);
+    Eigen::MatrixXcf A_float, B_float;
+    generate_random_matrix_pair(dim, A_float, B_float);
     CALL_SUBTEST_3(complex_qz(A_float, B_float));
+
+    // Test for double complex matrices
+    Eigen::MatrixXcd A_double, B_double;
+    generate_random_matrix_pair(dim, A_double, B_double);
     CALL_SUBTEST_4(complex_qz(A_double, B_double));
   }
 }
diff --git a/test/main.h b/test/main.h
index db4d484fb..fa7053e96 100644
--- a/test/main.h
+++ b/test/main.h
@@ -186,7 +186,7 @@ inline void on_temporary_creation(long int size, int) {
 
 namespace Eigen {
 static std::vector<std::string> g_test_stack;
-// level == 0 <=> abort if test fail
+// level == 0 <=> return 1 if test fail
 // level >= 1 <=> warning message to std::cerr if test fail
 static int g_test_level = 0;
 static int g_repeat = 1;
@@ -356,7 +356,7 @@ inline void verify_impl(bool condition, const char* testname, const char* file,
     const int test_stack_size = static_cast<int>(Eigen::g_test_stack.size());
     for (int i = test_stack_size - 1; i >= 0; --i) std::cerr << "  - " << Eigen::g_test_stack[i] << "\n";
     std::cerr << "\n";
-    if (Eigen::g_test_level == 0) abort();
+    if (Eigen::g_test_level == 0) exit(1);
   }
 }
 
@@ -858,6 +858,12 @@ inline void set_seed_from_string(const char* str) {
   g_has_set_seed = true;
 }
 
+inline void set_seed_from_time() {
+  using namespace std::chrono;
+  long long ns = duration_cast<nanoseconds>(high_resolution_clock::now().time_since_epoch()).count();
+  g_seed = static_cast<decltype(g_seed)>(ns);
+}
+
 int main(int argc, char* argv[]) {
   g_has_set_repeat = false;
   g_has_set_seed = false;
@@ -896,7 +902,7 @@ int main(int argc, char* argv[]) {
   char* env_EIGEN_SEED = getenv("EIGEN_SEED");
   if (!g_has_set_seed && env_EIGEN_SEED) set_seed_from_string(env_EIGEN_SEED);
 
-  if (!g_has_set_seed) g_seed = (unsigned int)time(NULL);
+  if (!g_has_set_seed) set_seed_from_time();
   if (!g_has_set_repeat) g_repeat = DEFAULT_REPEAT;
 
   std::cout << "Initializing random number generator with seed " << g_seed << std::endl;
diff --git a/unsupported/Eigen/src/Eigenvalues/ArpackSelfAdjointEigenSolver.h b/unsupported/Eigen/src/Eigenvalues/ArpackSelfAdjointEigenSolver.h
index 54db9bf29..bc21d94cc 100644
--- a/unsupported/Eigen/src/Eigenvalues/ArpackSelfAdjointEigenSolver.h
+++ b/unsupported/Eigen/src/Eigenvalues/ArpackSelfAdjointEigenSolver.h
@@ -454,8 +454,16 @@ ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>::compu
     }
   }
 
-  if (!(mode == 1 && isBempty) && !(mode == 2 && isBempty) && OP.info() != Success)
-    std::cout << "Error factoring matrix" << std::endl;
+  if (!(mode == 1 && isBempty) && !(mode == 2 && isBempty) && OP.info() != Success) {
+    m_info = OP.info() delete[] v;
+    delete[] iparam;
+    delete[] ipntr;
+    delete[] workd;
+    delete[] workl;
+    delete[] resid;
+    m_isInitialized = false;
+    return *this;
+  }
 
   do {
     internal::arpack_wrapper<Scalar, RealScalar>::saupd(&ido, bmat, &n, whch, &nev, &tol, resid, &ncv, v, &ldv, iparam,
@@ -572,7 +580,7 @@ ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>::compu
   delete[] workl;
   delete[] resid;
 
-  m_isInitialized = true;
+  m_isInitialized = (m_info == Success);
 
   return *this;
 }