The two-step spectral clustering method, which consists of the Laplacian eigenmap and a rounding step, is widely used method for graph partitioning. It can be seen as natural relaxation to NP-hard minimum ratio cut problem. In this paper, we study following central question: When able find global solution problem? First, provide condition that naturally depends on intra- intercluster connectivi...

abstract the objective of this study is evaluation of government’s optimum combination of policy instruments on per capita consumption of bread and the share of this product in food cost of families in different income classes. the minimization of changes in dead weight loss function is used in this study. by using boot strop method and on base of normal distribution for supply elasticity and d...

Sketching has emerged as a powerful technique for speeding up problems in numerical linear algebra, such as regression. In the overconstrained regression problem, one is given an n × d matrix A, with n d, as well as an n × 1 vector b, and one wants to find a vector x̂ so as to minimize the residual error ‖Ax− b‖2. Using the sketch and solve paradigm, one first computes S · A and S · b for a rand...

Although the Lagrangian method is a powerful dual search approach in integer programming, it often fails to identify an optimal solution of the primal problem. The p-th power Lagrangian method developed in this paper ooers a success guarantee for the dual search in generating an optimal solution of the primal integer programming problem in an equivalent setting via two key transformations. One ...