diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index 6122f51..8f89c54 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -1,15 +1,15 @@
-stages: 
- - build 
+stages:
+ - build
 
 ubuntu1604:
   stage: build
   image: docker-registry.csc.mpi-magdeburg.mpg.de:5000/ci-images/minimal/ubuntu:xenial
   script:
     - apt update && apt install --yes libopenblas-dev libblas-dev liblapack-dev
-    - mkdir -p build 
+    - mkdir -p build
     - cd build
-    - cmake ../ -DDEBUG=ON 
-    - make 
+    - cmake ../ -DDEBUG=ON
+    - make
     - make test
 
 ubuntu1804:
@@ -17,10 +17,10 @@ ubuntu1804:
   image: docker-registry.csc.mpi-magdeburg.mpg.de:5000/ci-images/minimal/ubuntu:bionic
   script:
     - apt update && apt install --yes libopenblas-dev libblas-dev liblapack-dev
-    - mkdir -p build 
+    - mkdir -p build
     - cd build
-    - cmake ../ -DDEBUG=ON 
-    - make 
+    - cmake ../ -DDEBUG=ON
+    - make
     - make test
 
 ubuntu2004:
@@ -30,29 +30,41 @@ ubuntu2004:
     - apt update && apt install --yes libopenblas-dev libblas-dev liblapack-dev
     - mkdir -p build
     - cd build
-    - cmake ../ -DDEBUG=ON 
-    - make 
+    - cmake ../ -DDEBUG=ON
+    - make
     - make test
-    
+
 centos7:
   stage: build
   image: docker-registry.csc.mpi-magdeburg.mpg.de:5000/ci-images/minimal/centos:7-base
   script:
-    - yum install -y cmake3 blas-devel lapack-devel 
+    - yum install -y cmake3 blas-devel lapack-devel
     - mkdir -p build
     - cd build
-    - cmake3 ../ -DDEBUG=ON 
-    - make 
+    - cmake3 ../ -DDEBUG=ON
+    - make
     - make test
 
 centos8:
   stage: build
   image: docker-registry.csc.mpi-magdeburg.mpg.de:5000/ci-images/minimal/centos:8-base
   script:
-    - yum install -y blas-devel lapack-devel 
+    - yum install -y blas-devel lapack-devel
     - mkdir -p build
     - cd build
-    - cmake ../ -DDEBUG=ON 
-    - make 
+    - cmake ../ -DDEBUG=ON
+    - make
     - make test
 
+cross-win32:
+  stage: build
+  image: docker-registry.csc.mpi-magdeburg.mpg.de:5000/ci-images/minimal/mingw:focal
+  script:
+    - bash ./tools/ci/cross-win32.sh
+
+cross-win64:
+  stage: build
+  image: docker-registry.csc.mpi-magdeburg.mpg.de:5000/ci-images/minimal/mingw:focal
+  script:
+    - bash ./tools/ci/cross-win64.sh
+
diff --git a/CHANGELOG b/CHANGELOG
index 279dbd7..1b0098c 100644
--- a/CHANGELOG
+++ b/CHANGELOG
@@ -1,3 +1,8 @@
+2022-02-04 Martin Koehler <koehlerm@mpi-magdeburg.mpg.de>
+
+    * Fix Tests on CYGWIN (GH #2)
+    * Enable MingW cross compiling
+
 2020-12-10  Martin Koehler <koehlerm@mpi-magdeburg.mpg.de>
 
     * Fix failed tchinc test on aarch64
diff --git a/CMakeLists.txt b/CMakeLists.txt
index da70d0e..180a93b 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1,6 +1,6 @@
 CMAKE_MINIMUM_REQUIRED(VERSION 3.1.0)
 CMAKE_POLICY(SET CMP0048 NEW)
-PROJECT(qrupdate-ng VERSION 1.1.4 LANGUAGES Fortran)
+PROJECT(qrupdate-ng VERSION 1.1.5 LANGUAGES Fortran)
 ENABLE_TESTING()
 
 # Options
diff --git a/CODE b/CODE
index 6aa07ee..8c1eb55 100644
--- a/CODE
+++ b/CODE
@@ -1,8 +1,8 @@
 # code.ini
 name: qrupdate-ng
 shortname: qrupdate-ng
-version: 1.1.4
-release-date: 2020-12-10
+version: 1.1.5
+release-date: 2022-02-04
 id: https://github.com/mpimd-csc/qrupdate-ng
 id-type: url
 author: Martin Koehler, Christian Himpe
diff --git a/INSTALL.md b/INSTALL.md
index fbc00e7..9719f6d 100644
--- a/INSTALL.md
+++ b/INSTALL.md
@@ -12,7 +12,7 @@ operating systems, which are supported by CMAKE, should work as well.
 
 Tested Fortran compilers:
 
- * GNU gfortran 4.8.5, 5.4, 7.3, 8.3, 9.2
+ * GNU gfortran 4.8.5, 5.4, 7.3, 8.3, 9.2, 9.3
  * Intel ifort 18.0.1
  * IBM XLF 16.1.1
 
@@ -77,4 +77,47 @@ and LAPACK could yield the following CMAKE call:
     cmake ../ -DBLAS_LIBRARIES=/home/user/software/libblas.a \
               -DLAPACK_LIBRARIES=/home/user/software/liblapack.a
 
+## Cross Compiling for Windows
+The build system supports cross compiling from Unix-like operating systems to
+Windows. Therefore, MingW64 (https://www.mingw-w64.org/) and
+Wine (https://www.winehq.org/) need to be present on the system. In case of
+Ubuntu 20.04 the following packages are required:
+* `mingw-w64`, `mingw-w64-i686-dev` , `mingw-w64-x86-64-dev`
+* `gfortran-mingw-w64-i686`, `gfortran-mingw-w64-x86-64`
+* `wine32`, `wine64`
+* `wget`
+
+Furthermore, BLAS and LAPACK are required in the MingW installation. If this is
+not the case, the reference BLAS and LAPACK library can be installed via
+```shell
+ bash ./tools/install-lapack-mingw-i686.sh
+```
+for the Windows 32-bit environment, and  using
+```shelll
+bash ./tools/install-lapack-mingw-x86_64.sh
+```
+for the Windows 64-bit environment.
+
+The Windows 32-bit  library can then be compiled using
+```shell
+cmake -S . -B build.win32 \
+      -DCMAKE_TOOLCHAIN_FILE=$(pwd)/cmake/mingw-w32-i686.cmake \
+      -DBUILD_SHARED_LIBS=ON \
+      -DCMAKE_INSTALL_PREFIX=$(pwd)/install-win32
+make -C build.win32 all
+(cd build.win32; ctest -V )
+make -C build.win32 install
+```
+
+In case of the 64-bit Windows library, the build process looks like
+```shell
+cmake -S . -B build.win64 \
+      -DCMAKE_TOOLCHAIN_FILE=$(pwd)/cmake/mingw-w64-x86_64.cmake \
+      -DBUILD_SHARED_LIBS=ON \
+      -DCMAKE_INSTALL_PREFIX=$(pwd)/install-win32
+make -C build.win64 all
+(cd build.win64; ctest -V )
+make -C build.win64 install
+```
+
 
diff --git a/README.md b/README.md
index a7ca411..53c915a 100644
--- a/README.md
+++ b/README.md
@@ -2,8 +2,9 @@ qrupdate-ng: A Library for Fast Updating of QR and Cholesky Decompositions
 ==========================================================================
 
 * License: GPL-3.0-or-later (opensource.org/licenses/GPL-3.0)
-* Version: 1.1.4 (2020-12-10)
+* Version: 1.1.5 (2022-02-04)
 * Authors: M. Koehler (0000-0003-2338-9904), C. Himpe (0000-0003-2194-6754)
+* Original Author: Jaroslav Hajek (VZLU Prague)
 * Summary: A FORTRAN library for rank-1 matrix decomposition updates
 
 ## Supported Matrix Decompositions
diff --git a/cmake/mingw-w32-i686.cmake b/cmake/mingw-w32-i686.cmake
new file mode 100644
index 0000000..dac2eba
--- /dev/null
+++ b/cmake/mingw-w32-i686.cmake
@@ -0,0 +1,36 @@
+# Sample toolchain file for building for Windows from an Ubuntu Linux system.
+#
+# Typical usage:
+#    *) install cross compiler: `sudo apt-get install mingw-w64` or `brew install mingw-w64` on macOS
+#    *) cmake -DCMAKE_TOOLCHAIN_FILE=~/mingw-w64-x86_64.cmake -G Ninja -B build -S .
+#    *) ninja -C build
+
+
+set(CMAKE_SYSTEM_NAME Windows)
+set(TOOLCHAIN_PREFIX i686-w64-mingw32)
+
+# cross compilers to use for C, C++ and Fortran
+set(CMAKE_C_COMPILER ${TOOLCHAIN_PREFIX}-gcc)
+set(CMAKE_CXX_COMPILER ${TOOLCHAIN_PREFIX}-g++)
+set(CMAKE_Fortran_COMPILER ${TOOLCHAIN_PREFIX}-gfortran)
+set(CMAKE_RC_COMPILER ${TOOLCHAIN_PREFIX}-windres)
+
+# target environment on the build host system
+set(CMAKE_FIND_ROOT_PATH /usr/${TOOLCHAIN_PREFIX} ${CMAKE_SOURCE_DIR}/tools/${TOOLCHAIN_PREFIX})
+
+# modify default behavior of FIND_XXX() commands
+set(CMAKE_FIND_ROOT_PATH_MODE_PROGRAM NEVER)
+set(CMAKE_FIND_ROOT_PATH_MODE_LIBRARY ONLY)
+set(CMAKE_FIND_ROOT_PATH_MODE_INCLUDE ONLY)
+
+set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS}")
+set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+set(CMAKE_Fortran_FLAGS "${CMAKE_Fortran_FLAGS}")
+
+set(Fortran_LOCAL_FLAGS "-static")
+set(C_LOCAL_FLAGS "-static")
+set(CXX_LOCAL_FLAGS "-static")
+
+#set(CMAKE_SHARED_LINKER_FLAGS "${CMAKE_SHARED_LINKER_FLAGS} -static-libgcc -Wl,-Bstatic -lgfortran -lquadmath -Wl,-Bdynamic")
+#set(CMAKE_EXE_LINKER_FLAGS " -static-libgcc -Wl,-Bstatic -lgfortran -lquadmath -Wl,-Bdynamic ${CMAKE_EXE_LINKER_FLAGS} ")
+
diff --git a/cmake/mingw-w64-x86_64.cmake b/cmake/mingw-w64-x86_64.cmake
new file mode 100644
index 0000000..a9de097
--- /dev/null
+++ b/cmake/mingw-w64-x86_64.cmake
@@ -0,0 +1,35 @@
+# Sample toolchain file for building for Windows from an Ubuntu Linux system.
+#
+# Typical usage:
+#    *) install cross compiler: `sudo apt-get install mingw-w64` or `brew install mingw-w64` on macOS
+#    *) cmake -DCMAKE_TOOLCHAIN_FILE=~/mingw-w64-x86_64.cmake -G Ninja -B build -S .
+#    *) ninja -C build
+
+
+set(CMAKE_SYSTEM_NAME Windows)
+set(TOOLCHAIN_PREFIX x86_64-w64-mingw32)
+
+# cross compilers to use for C, C++ and Fortran
+set(CMAKE_C_COMPILER ${TOOLCHAIN_PREFIX}-gcc)
+set(CMAKE_CXX_COMPILER ${TOOLCHAIN_PREFIX}-g++)
+set(CMAKE_Fortran_COMPILER ${TOOLCHAIN_PREFIX}-gfortran)
+set(CMAKE_RC_COMPILER ${TOOLCHAIN_PREFIX}-windres)
+
+# target environment on the build host system
+set(CMAKE_FIND_ROOT_PATH /usr/${TOOLCHAIN_PREFIX} ${CMAKE_SOURCE_DIR}/tools/${TOOLCHAIN_PREFIX})
+
+# modify default behavior of FIND_XXX() commands
+set(CMAKE_FIND_ROOT_PATH_MODE_PROGRAM NEVER)
+set(CMAKE_FIND_ROOT_PATH_MODE_LIBRARY ONLY)
+set(CMAKE_FIND_ROOT_PATH_MODE_INCLUDE ONLY)
+
+set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} ")
+set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ")
+set(CMAKE_Fortran_FLAGS "${CMAKE_Fortran_FLAGS} ")
+
+set(Fortran_LOCAL_FLAGS "-static")
+set(C_LOCAL_FLAGS "-static")
+set(CXX_LOCAL_FLAGS "-static")
+
+# set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} -static -Os")
+# set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -static -Os")
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
index 4fa1d2c..dd27d30 100644
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -16,11 +16,64 @@ SET(TEST_PRGM
     tqrinc
     tqrinr
     tqrshc
-)
+    )
+
+
+IF ( CMAKE_CROSSCOMPILING AND CMAKE_SYSTEM_NAME MATCHES Windows )
+    SET(CMAKE_Fortran_FLAGS "${CMAKE_Fortran_FLAGS} ${Fortran_LOCAL_FLAGS}")
+    FIND_PROGRAM(WINE NAMES wine wine32 wine64)
+    IF ( NOT WINE )
+        MESSAGE(FATAL_ERROR "Wine not found")
+    ELSE()
+        MESSAGE(STATUS "Wine found: ${WINE}")
+    ENDIF()
+
+    EXECUTE_PROCESS(COMMAND ${CMAKE_C_COMPILER} -print-search-dirs
+        COMMAND grep programs
+        COMMAND cut -d= -f2
+        COMMAND sed -e "s/:/;/g"
+        COMMAND tr -d "\n" OUTPUT_VARIABLE WINEPATH_TMP)
+    SET(WINEPATH)
+    SET(ENVPATH_TMP "$ENV{WINEPATH}")
+    FOREACH ( P IN LISTS ENVPATH_TMP)
+        SET(WINEPATH "${WINEPATH}\\;${P}")
+    ENDFOREACH()
+    FOREACH ( P IN LISTS CMAKE_FIND_ROOT_PATH )
+        SET(WINEPATH "${WINEPATH}\\;${P}/bin")
+        SET(WINEPATH "${WINEPATH}\\;${P}/lib")
+    ENDFOREACH()
+
+
+    FOREACH ( P IN LISTS WINEPATH_TMP )
+        SET(WINEPATH "${WINEPATH}\\;${P}")
+    ENDFOREACH()
+
+    SET(WINEPATH "${CMAKE_BINARY_DIR}/src\\;${WINEPATH}")
+    MESSAGE(STATUS "Setting WINEPATH for tests to ${WINEPATH}")
+ENDIF()
+
+IF (CMAKE_SYSTEM_NAME MATCHES "CYGWIN")
+    MESSAGE(STATUS "CYGWIN build")
+    MESSAGE("Set additional PATH for tests to ${CMAKE_BINARY_DIR}/src:/usr/lib/lapack")
+    SET(ADDPATH  "${CMAKE_BINARY_DIR}/src:/usr/lib/lapack")
+ENDIF()
+
 
 FOREACH(TEST_CODE ${TEST_PRGM})
     ADD_EXECUTABLE(${TEST_CODE} ${TEST_CODE}.f)
-    TARGET_LINK_LIBRARIES(${TEST_CODE} utils qrupdate)
-    ADD_TEST(NAME test_${TEST_CODE} COMMAND ${CMAKE_CURRENT_BINARY_DIR}/${TEST_CODE})
+    TARGET_LINK_LIBRARIES(${TEST_CODE} utils qrupdate )
+    IF ( CMAKE_CROSSCOMPILING )
+        IF ( CMAKE_SYSTEM_NAME MATCHES Windows)
+            ADD_TEST(NAME test_${TEST_CODE} COMMAND ${WINE} ${CMAKE_CURRENT_BINARY_DIR}/${TEST_CODE}${CMAKE_EXECUTABLE_SUFFIX})
+            SET_TESTS_PROPERTIES(test_${TEST_CODE} PROPERTIES ENVIRONMENT "WINEPATH=${WINEPATH}")
+        ELSE()
+            MESSAGE(WARNING "Cross-Compile checks are only possible from Linux to Windows.")
+        ENDIF()
+    ELSE ()
+        ADD_TEST(NAME test_${TEST_CODE} COMMAND ${CMAKE_CURRENT_BINARY_DIR}/${TEST_CODE})
+        IF ( ADDPATH )
+            SET_TESTS_PROPERTIES(test_${TEST_CODE} PROPERTIES ENVIRONMENT "PATH=${ADDPATH}:$ENV{PATH}")
+        ENDIF()
+    ENDIF()
 ENDFOREACH()
 
diff --git a/tools/ci/cross-win32.sh b/tools/ci/cross-win32.sh
new file mode 100644
index 0000000..dfcf056
--- /dev/null
+++ b/tools/ci/cross-win32.sh
@@ -0,0 +1,7 @@
+#!/bin/bash
+set -x
+(cd tools/; bash install-lapack-mingw-i686.sh)
+cmake -S . -B build.win32 -DCMAKE_TOOLCHAIN_FILE=$(pwd)/cmake/mingw-w32-i686.cmake -DBUILD_SHARED_LIBS=ON
+make -C build.win32 all
+(cd build.win32; ctest -V )
+
diff --git a/tools/ci/cross-win64.sh b/tools/ci/cross-win64.sh
new file mode 100644
index 0000000..87e2f32
--- /dev/null
+++ b/tools/ci/cross-win64.sh
@@ -0,0 +1,7 @@
+#!/bin/bash
+set -x
+(cd tools/; bash install-lapack-mingw-x86_64.sh)
+cmake -S . -B build.win64 -DCMAKE_TOOLCHAIN_FILE=$(pwd)/cmake/mingw-w64-x86_64.cmake -DBUILD_SHARED_LIBS=ON
+make -C build.win64 all
+(cd build.win64; ctest -V )
+
diff --git a/tools/install-lapack-mingw-i686.sh b/tools/install-lapack-mingw-i686.sh
new file mode 100644
index 0000000..501d4c4
--- /dev/null
+++ b/tools/install-lapack-mingw-i686.sh
@@ -0,0 +1,13 @@
+#!/bin/bash
+set -x
+
+[ -d build-lapack-win32 ] && rm -rf build-lapack-win32
+
+[ -e v3.10.0.tar.gz ] || wget -c https://github.com/Reference-LAPACK/lapack/archive/refs/tags/v3.10.0.tar.gz
+tar xf v3.10.0.tar.gz
+cmake -S lapack-3.10.0 -B build-lapack-win32 \
+    -DCMAKE_TOOLCHAIN_FILE=$(pwd)/../cmake/mingw-w32-i686.cmake \
+    -DBUILD_SHARED_LIBS=ON \
+    -DCMAKE_INSTALL_PREFIX=`dirname $(realpath $0)`/i686-w64-mingw32
+make -C build-lapack-win32 -j 4
+make -C build-lapack-win32 install
diff --git a/tools/install-lapack-mingw-x86_64.sh b/tools/install-lapack-mingw-x86_64.sh
new file mode 100644
index 0000000..a8d0dca
--- /dev/null
+++ b/tools/install-lapack-mingw-x86_64.sh
@@ -0,0 +1,15 @@
+#!/bin/bash
+
+#!/bin/bash
+set -x
+
+[ -d build-lapack-win64 ] && rm -rf build-lapack-win64
+
+[ -e v3.10.0.tar.gz ] || wget -c https://github.com/Reference-LAPACK/lapack/archive/refs/tags/v3.10.0.tar.gz
+tar xf v3.10.0.tar.gz
+cmake -S lapack-3.10.0 -B build-lapack-win64 \
+    -DCMAKE_TOOLCHAIN_FILE=$(pwd)/../cmake/mingw-w64-x86_64.cmake \
+    -DBUILD_SHARED_LIBS=ON \
+    -DCMAKE_INSTALL_PREFIX=`dirname $(realpath $0)`/x86_64-w64-mingw32
+make -C build-lapack-win64 -j 4
+make -C build-lapack-win64 install