This paper adapts the recently developed rigorous application of supersymmetric transfer matrix approach for Hermitian 1d band matrices to case orthogonal symmetry. We consider N×N block consisting W×W random Gaussian blocks (parametrized by j,k∈Λ=[1,n]∩Z, N=nW) with a fixed entry’s variance Jjk=W−1(δj,k+βΔj,k) in each block. Considering limit W,n→∞, we prove that behaviour second correlation f...

Emergence of localized eigenvectors can cause a failure of standard spectral method for graph partitioning. The spectral method using the non-backtracking matrix was proposed as a way to overcome this problem. The numerical experiments on several examples of real networks show that, indeed, the non-backtracking matrix does not exhibit localization of eigenvectors. We show that, however, localiz...

a class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional bratu's problem are presented. the local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. the inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. associated bound...

In this chapter the use of compactly-supported radial basis functions for surface reconstruction is described. To solve the problem of reconstruction or volume data generation specially designed software is employed. Time performance of the algorithm is investigated. Thanks to the efficient octree algorithm used in this study, the resulting matrix is a band diagonal matrix that reduces computat...