Abstract. The method to generalize handling the nodal constraint in the finite element method into the stiffness matrix to the multipoint constraint is extended when the multipoint constraint is not full rank. It is also extended when the matrix is asymmetric.
Abstract. QR decomposition with pivot selection is known to be less accurate as low rank approximation than singular value decomposition, but it is often used because the calculation amount is smaller than SVD. The minimum upper bound of the truncation error of QR decomposition with pivot selection is estimated accurately in case r = n − 1 of approximating m × n (m ≥ n) matrix to matrix whose rank is r so it is introduced in this paper.