When formula_25, columns formula_26 should be concatenated and solved for simultaneously. Set formula_27  Using the QR algorithm, the real Schur decompositions in step 1 require approximately formula_28 flops, so that the overall computational cost is formula_29. In the special case where formula_30 and formula_31 is symmetric, the solution formula_5 will also be symmetric. This symmetry can be exploited so that formula_24 is found more efficiently in step 3 of the algorithm. The Hessenberg–Schur algorithm replaces the decomposition formula_34 in step 1 with the decomposition formula_35, where formula_36 is an upper-Hessenberg matrix. This leads to a system of the form formula_37 that can be solved using forward substitution. The advantage of this approach is that formula_35 can be found using Householder reflections at a cost of formula_39 flops, compared to the formula_40 flops required to compute the real Schur decomposition of formula_2. The subroutines required for the Hessenberg-Schur variant of the Bartels–Stewart algorithm are implemented in the SLICOT library. These are used in the MATLAB control system toolbox. For large systems, the formula_42 cost of the Bartels–Stewart algorithm can be prohibitive. When formula_2 and formula_3 are sparse or structured, so that linear solves and matrix vector multiplies involving them are efficient, iterative algorithms can potentially perform better. These include projection-based methods, which use Krylov subspace iterations, methods based on the alternating direction implicit (ADI) iteration, and hybridizations that involve both projection and ADI. Iterative methods can also be used to directly construct low rank approximations to formula_5 when solving formula_46. Nautanwa (Assembly constituency)  Nautanwa is a constituency of the Uttar Pradesh Legislative Assembly covering the city of Nautanwa in the Maharajganj district of Uttar Pradesh, India. Nautanwa is one of five assembly constituencies in the Maharajganj (Lok Sabha constituency). Since 2008, this assembly constituency is numbered 316 amongst 403 constituencies. Currently this seat belongs to Independent candidate Aman Mani Tripathi who won in last Assembly election of 2017 Uttar Pradesh Legislative Elections defeating Indian National Congress candidate Kunwar Kaushal Kishore Singh by a margin of 32,256 votes. Shuchi  Shuchi is a given name, used as a female name in India and China and as a male name in Japan.