diff --git a/src/atlas/interpolation/Cache.h b/src/atlas/interpolation/Cache.h
index 2e70f827c..8c2b9d9bf 100644
--- a/src/atlas/interpolation/Cache.h
+++ b/src/atlas/interpolation/Cache.h
@@ -17,8 +17,8 @@
 #include "eckit/filesystem/PathName.h"
 #include "eckit/io/Buffer.h"
 
-#include "eckit/linalg/SparseMatrix.h"
 
+#include "atlas/linalg/SparseMatrix.h"
 #include "atlas/runtime/Exception.h"
 #include "atlas/util/KDTree.h"
 
@@ -82,7 +82,7 @@ class Cache {
 
 class MatrixCacheEntry : public InterpolationCacheEntry {
 public:
-    using Matrix = eckit::linalg::SparseMatrix;
+    using Matrix = atlas::linalg::SparseMatrix;
     ~MatrixCacheEntry() override;
     MatrixCacheEntry(const Matrix* matrix, const std::string& uid = ""): matrix_{matrix}, uid_(uid) {
         ATLAS_ASSERT(matrix_ != nullptr);
diff --git a/src/atlas/interpolation/method/Method.h b/src/atlas/interpolation/method/Method.h
index 7e52d5bf3..5b37ca25c 100644
--- a/src/atlas/interpolation/method/Method.h
+++ b/src/atlas/interpolation/method/Method.h
@@ -16,10 +16,10 @@
 
 #include "atlas/interpolation/Cache.h"
 #include "atlas/interpolation/NonLinear.h"
+#include "atlas/linalg/SparseMatrix.h"
 #include "atlas/util/Metadata.h"
 #include "atlas/util/Object.h"
 #include "eckit/config/Configuration.h"
-#include "eckit/linalg/SparseMatrix.h"
 
 namespace atlas {
 class Field;
@@ -87,7 +87,7 @@ class Method : public util::Object {
 
     using Triplet  = eckit::linalg::Triplet;
     using Triplets = std::vector<Triplet>;
-    using Matrix   = eckit::linalg::SparseMatrix;
+    using Matrix   = atlas::linalg::SparseMatrix;
 
     static void normalise(Triplets& triplets);
 
diff --git a/src/atlas/interpolation/method/binning/Binning.cc b/src/atlas/interpolation/method/binning/Binning.cc
index f5a6b0743..902072f4f 100644
--- a/src/atlas/interpolation/method/binning/Binning.cc
+++ b/src/atlas/interpolation/method/binning/Binning.cc
@@ -12,12 +12,12 @@
 #include "atlas/interpolation/Interpolation.h"
 #include "atlas/interpolation/method/binning/Binning.h"
 #include "atlas/interpolation/method/MethodFactory.h"
+#include "atlas/linalg/SparseMatrix.h"
 #include "atlas/mesh.h"
 #include "atlas/mesh/actions/GetCubedSphereNodalArea.h"
 #include "atlas/runtime/Trace.h"
 
 #include "eckit/config/LocalConfiguration.h"
-#include "eckit/linalg/SparseMatrix.h"
 #include "eckit/linalg/Triplet.h"
 #include "eckit/mpi/Comm.h"
 
@@ -58,7 +58,7 @@ void Binning::do_setup(const FunctionSpace& source,
 
   using Index = eckit::linalg::Index;
   using Triplet = eckit::linalg::Triplet;
-  using SMatrix = eckit::linalg::SparseMatrix;
+  using SMatrix = atlas::linalg::SparseMatrix;
 
   source_ = source;
   target_ = target;
diff --git a/src/atlas/interpolation/method/knn/GridBoxMaximum.cc b/src/atlas/interpolation/method/knn/GridBoxMaximum.cc
index 8ca86672a..6a3435478 100644
--- a/src/atlas/interpolation/method/knn/GridBoxMaximum.cc
+++ b/src/atlas/interpolation/method/knn/GridBoxMaximum.cc
@@ -61,7 +61,7 @@ void GridBoxMaximum::do_execute(const Field& source, Field& target, Metadata&) c
 
     if (!matrixFree_) {
         const Matrix& m = matrix();
-        Matrix::const_iterator k(m);
+        Matrix::const_iterator k = m.begin();
 
         for (decltype(m.rows()) i = 0, j = 0; i < m.rows(); ++i) {
             double max = std::numeric_limits<double>::lowest();
diff --git a/src/atlas/interpolation/method/unstructured/ConservativeSphericalPolygonInterpolation.cc b/src/atlas/interpolation/method/unstructured/ConservativeSphericalPolygonInterpolation.cc
index d1ea5addf..334b65422 100644
--- a/src/atlas/interpolation/method/unstructured/ConservativeSphericalPolygonInterpolation.cc
+++ b/src/atlas/interpolation/method/unstructured/ConservativeSphericalPolygonInterpolation.cc
@@ -1248,7 +1248,7 @@ void ConservativeSphericalPolygonInterpolation::intersect_polygons(const CSPolyg
     }
 }
 
-eckit::linalg::SparseMatrix ConservativeSphericalPolygonInterpolation::compute_1st_order_matrix() {
+atlas::linalg::SparseMatrix ConservativeSphericalPolygonInterpolation::compute_1st_order_matrix() {
     ATLAS_TRACE("ConservativeMethod::setup: build cons-1 interpolant matrix");
     ATLAS_ASSERT(not matrix_free_);
     Triplets triplets;
@@ -1358,7 +1358,7 @@ eckit::linalg::SparseMatrix ConservativeSphericalPolygonInterpolation::compute_1
     return Matrix(n_tpoints_, n_spoints_, triplets);
 }
 
-eckit::linalg::SparseMatrix ConservativeSphericalPolygonInterpolation::compute_2nd_order_matrix() {
+atlas::linalg::SparseMatrix ConservativeSphericalPolygonInterpolation::compute_2nd_order_matrix() {
     ATLAS_TRACE("ConservativeMethod::setup: build cons-2 interpolant matrix");
     ATLAS_ASSERT(not matrix_free_);
     const auto& src_points_ = data_->src_points_;
diff --git a/src/atlas/interpolation/nonlinear/Missing.cc b/src/atlas/interpolation/nonlinear/Missing.cc
index 1258f9fdc..47c35f6b6 100644
--- a/src/atlas/interpolation/nonlinear/Missing.cc
+++ b/src/atlas/interpolation/nonlinear/Missing.cc
@@ -81,7 +81,7 @@ bool MissingIfAllMissing::executeT(NonLinear::Matrix& W, const Field& field) con
     bool zeros = false;
 
     Size i = 0;
-    Matrix::iterator it(W);
+    Matrix::iterator it = W.begin();
     for (Size r = 0; r < W.rows(); ++r) {
         const Matrix::iterator end = W.end(r);
 
@@ -128,6 +128,9 @@ bool MissingIfAllMissing::executeT(NonLinear::Matrix& W, const Field& field) con
             modif = true;
         }
     }
+    if (modif) {
+        W.setDeviceNeedsUpdate(true);
+    }
 
     if (zeros && missingValue.isnan()) {
         W.prune(0.);
@@ -161,7 +164,7 @@ bool MissingIfAnyMissing::executeT(NonLinear::Matrix& W, const Field& field) con
     bool zeros = false;
 
     Size i = 0;
-    Matrix::iterator it(W);
+    Matrix::iterator it = W.begin();
     for (Size r = 0; r < W.rows(); ++r) {
         const Matrix::iterator end = W.end(r);
 
@@ -195,6 +198,9 @@ bool MissingIfAnyMissing::executeT(NonLinear::Matrix& W, const Field& field) con
             modif = true;
         }
     }
+    if (modif) {
+        W.setDeviceNeedsUpdate(true);
+    }
 
     if (zeros && missingValue.isnan()) {
         W.prune(0.);
@@ -228,7 +234,7 @@ bool MissingIfHeaviestMissing::executeT(NonLinear::Matrix& W, const Field& field
     bool zeros = false;
 
     Size i = 0;
-    Matrix::iterator it(W);
+    Matrix::iterator it = W.begin();
     for (Size r = 0; r < W.rows(); ++r) {
         const Matrix::iterator end = W.end(r);
 
@@ -282,6 +288,9 @@ bool MissingIfHeaviestMissing::executeT(NonLinear::Matrix& W, const Field& field
             modif = true;
         }
     }
+    if (modif) {
+        W.setDeviceNeedsUpdate(true);
+    }
 
     if (zeros && missingValue.isnan()) {
         W.prune(0.);
diff --git a/src/atlas/interpolation/nonlinear/NonLinear.h b/src/atlas/interpolation/nonlinear/NonLinear.h
index dce24441e..7ce865434 100644
--- a/src/atlas/interpolation/nonlinear/NonLinear.h
+++ b/src/atlas/interpolation/nonlinear/NonLinear.h
@@ -16,10 +16,10 @@
 #include <type_traits>
 
 #include "eckit/config/Parametrisation.h"
-#include "eckit/linalg/SparseMatrix.h"
 
 #include "atlas/array.h"
 #include "atlas/field/Field.h"
+#include "atlas/linalg/SparseMatrix.h"
 #include "atlas/runtime/Exception.h"
 #include "atlas/util/Factory.h"
 #include "atlas/util/ObjectHandle.h"
@@ -37,9 +37,9 @@ namespace nonlinear {
 class NonLinear : public util::Object {
 public:
     using Config = eckit::Parametrisation;
-    using Matrix = eckit::linalg::SparseMatrix;
-    using Scalar = eckit::linalg::Scalar;
-    using Size   = eckit::linalg::Size;
+    using Matrix = atlas::linalg::SparseMatrix;
+    using Scalar = atlas::linalg::SparseMatrix::Scalar;
+    using Size   = atlas::linalg::SparseMatrix::Size;
 
     /**
      * @brief ctor
diff --git a/src/atlas/linalg/sparse/SparseMatrixMultiply.h b/src/atlas/linalg/sparse/SparseMatrixMultiply.h
index d1776975b..6d923ebb0 100644
--- a/src/atlas/linalg/sparse/SparseMatrixMultiply.h
+++ b/src/atlas/linalg/sparse/SparseMatrixMultiply.h
@@ -11,9 +11,9 @@
 #pragma once
 
 #include "eckit/config/Configuration.h"
-#include "eckit/linalg/SparseMatrix.h"
 
 #include "atlas/linalg/Indexing.h"
+#include "atlas/linalg/SparseMatrix.h"
 #include "atlas/linalg/View.h"
 #include "atlas/linalg/sparse/Backend.h"
 #include "atlas/runtime/Exception.h"
@@ -22,7 +22,6 @@
 namespace atlas {
 namespace linalg {
 
-using SparseMatrix  = eckit::linalg::SparseMatrix;
 using Configuration = eckit::Configuration;
 
 template <typename Matrix, typename SourceView, typename TargetView>
diff --git a/src/atlas/linalg/sparse/SparseMatrixMultiply_EckitLinalg.cc b/src/atlas/linalg/sparse/SparseMatrixMultiply_EckitLinalg.cc
index 72d55c1a9..b9bb1f9b4 100644
--- a/src/atlas/linalg/sparse/SparseMatrixMultiply_EckitLinalg.cc
+++ b/src/atlas/linalg/sparse/SparseMatrixMultiply_EckitLinalg.cc
@@ -70,7 +70,7 @@ void SparseMatrixMultiply<backend::eckit_linalg, Indexing::layout_right, 1, cons
     ATLAS_ASSERT(tgt.contiguous());
     eckit::linalg::Vector v_src(src.data(), src.size());
     eckit::linalg::Vector v_tgt(tgt.data(), tgt.size());
-    eckit_linalg_backend(config).spmv(W, v_src, v_tgt);
+    eckit_linalg_backend(config).spmv(W.host_matrix(), v_src, v_tgt);
 }
 
 void SparseMatrixMultiply<backend::eckit_linalg, Indexing::layout_right, 2, const double, double>::apply(
@@ -81,7 +81,7 @@ void SparseMatrixMultiply<backend::eckit_linalg, Indexing::layout_right, 2, cons
     ATLAS_ASSERT(tgt.shape(1) >= W.rows());
     eckit::linalg::Matrix m_src(src.data(), src.shape(1), src.shape(0));
     eckit::linalg::Matrix m_tgt(tgt.data(), tgt.shape(1), tgt.shape(0));
-    eckit_linalg_backend(config).spmm(W, m_src, m_tgt);
+    eckit_linalg_backend(config).spmm(W.host_matrix(), m_src, m_tgt);
 }
 
 void SparseMatrixMultiply<backend::eckit_linalg, Indexing::layout_left, 1, const double, double>::apply(
diff --git a/src/tests/interpolation/test_interpolation_finite_element_cached.cc b/src/tests/interpolation/test_interpolation_finite_element_cached.cc
index 99d9803c6..971ffd90d 100644
--- a/src/tests/interpolation/test_interpolation_finite_element_cached.cc
+++ b/src/tests/interpolation/test_interpolation_finite_element_cached.cc
@@ -106,7 +106,7 @@ CASE("extract cache, copy it, and move it for use") {
 
     set_field(field_source, grid_source, func);
 
-    eckit::linalg::SparseMatrix matrix = get_or_create_cache(grid_source, grid_target).matrix();
+    atlas::linalg::SparseMatrix matrix = get_or_create_cache(grid_source, grid_target).matrix();
 
     EXPECT(not matrix.empty());
 
@@ -133,7 +133,7 @@ CASE("extract cache, copy it, and pass non-owning pointer") {
 
     set_field(field_source, grid_source, func);
 
-    eckit::linalg::SparseMatrix matrix = get_or_create_cache(grid_source, grid_target).matrix();
+    atlas::linalg::SparseMatrix matrix = get_or_create_cache(grid_source, grid_target).matrix();
 
     EXPECT(not matrix.empty());