diff --git a/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h b/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h
new file mode 100644
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+++ b/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h
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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_SOLVEWITHGUESS_H
+#define EIGEN_SOLVEWITHGUESS_H
+
+namespace Eigen {
+
+template<typename Decomposition, typename RhsType, typename GuessType> class SolveWithGuess;
+  
+/** \class SolveWithGuess
+  * \ingroup IterativeLinearSolvers_Module
+  *
+  * \brief Pseudo expression representing a solving operation
+  *
+  * \tparam Decomposition the type of the matrix or decomposion object
+  * \tparam Rhstype the type of the right-hand side
+  *
+  * This class represents an expression of A.solve(B)
+  * and most of the time this is the only way it is used.
+  *
+  */
+namespace internal {
+
+
+template<typename Decomposition, typename RhsType, typename GuessType>
+struct traits<SolveWithGuess<Decomposition, RhsType, GuessType> >
+  : traits<Solve<Decomposition,RhsType> >
+{};
+
+}
+
+
+template<typename Decomposition, typename RhsType, typename GuessType>
+class SolveWithGuess : public internal::generic_xpr_base<SolveWithGuess<Decomposition,RhsType,GuessType>, MatrixXpr, typename internal::traits<RhsType>::StorageKind>::type
+{
+public:
+  typedef typename internal::traits<SolveWithGuess>::Scalar Scalar;
+  typedef typename internal::traits<SolveWithGuess>::PlainObject PlainObject;
+  typedef typename internal::generic_xpr_base<SolveWithGuess<Decomposition,RhsType,GuessType>, MatrixXpr, typename internal::traits<RhsType>::StorageKind>::type Base;
+  typedef typename internal::ref_selector<SolveWithGuess>::type Nested;
+  
+  SolveWithGuess(const Decomposition &dec, const RhsType &rhs, const GuessType &guess)
+    : m_dec(dec), m_rhs(rhs), m_guess(guess)
+  {}
+  
+  EIGEN_DEVICE_FUNC Index rows() const { return m_dec.cols(); }
+  EIGEN_DEVICE_FUNC Index cols() const { return m_rhs.cols(); }
+
+  EIGEN_DEVICE_FUNC const Decomposition& dec()   const { return m_dec; }
+  EIGEN_DEVICE_FUNC const RhsType&       rhs()   const { return m_rhs; }
+  EIGEN_DEVICE_FUNC const GuessType&     guess() const { return m_guess; }
+
+protected:
+  const Decomposition &m_dec;
+  const RhsType       &m_rhs;
+  const GuessType     &m_guess;
+  
+private:
+  Scalar coeff(Index row, Index col) const;
+  Scalar coeff(Index i) const;
+};
+
+namespace internal {
+
+// Evaluator of SolveWithGuess -> eval into a temporary
+template<typename Decomposition, typename RhsType, typename GuessType>
+struct evaluator<SolveWithGuess<Decomposition,RhsType, GuessType> >
+  : public evaluator<typename SolveWithGuess<Decomposition,RhsType,GuessType>::PlainObject>
+{
+  typedef SolveWithGuess<Decomposition,RhsType,GuessType> SolveType;
+  typedef typename SolveType::PlainObject PlainObject;
+  typedef evaluator<PlainObject> Base;
+
+  evaluator(const SolveType& solve)
+    : m_result(solve.rows(), solve.cols())
+  {
+    ::new (static_cast<Base*>(this)) Base(m_result);
+    m_result = solve.guess();
+    solve.dec()._solve_with_guess_impl(solve.rhs(), m_result);
+  }
+  
+protected:  
+  PlainObject m_result;
+};
+
+// Specialization for "dst = dec.solveWithGuess(rhs)"
+// NOTE we need to specialize it for Dense2Dense to avoid ambiguous specialization error and a Sparse2Sparse specialization must exist somewhere
+template<typename DstXprType, typename DecType, typename RhsType, typename GuessType, typename Scalar>
+struct Assignment<DstXprType, SolveWithGuess<DecType,RhsType,GuessType>, internal::assign_op<Scalar,Scalar>, Dense2Dense>
+{
+  typedef SolveWithGuess<DecType,RhsType,GuessType> SrcXprType;
+  static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
+  {
+    Index dstRows = src.rows();
+    Index dstCols = src.cols();
+    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
+      dst.resize(dstRows, dstCols);
+
+    dst = src.guess();
+    src.dec()._solve_with_guess_impl(src.rhs(), dst/*, src.guess()*/);
+  }
+};
+
+} // end namepsace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_SOLVEWITHGUESS_H