In this paper we define multiplication between intuitionistic fuzzy matrices (IFMs) and we derive the conditions for a block IFM to be regular. Also a method to find the generalized inverse of it with the help of the generalized inverses of the blocks of the original matrix is described. Again, it is shown that a block intuitionistic fuzzy matrix can be decomposed into an upper triangular idemp...

Symmetric multiscale collocation methods with radial basis functions allow approximation of the solution of a partial differential equation, even if the right-hand side is only known at scattered data points, without needing to generate a grid. However, the benefit of a guaranteed symmetric positive definite block system comes at a high computational cost. In particular, the condition number an...

The FETI-DP domain decomposition method is extended to address the iterative solution of a class of indefinite problems of the form (K−σM)x = b, and a class of complex problems of the form (K − σM + iσD)x = b, where K, M, and D are three real symmetric positive semi-definite matrices arising from the finite element discretization of either second-order elastodynamic problems or fourth-order pla...

We study numerical methods for finding the maximal symmetric positive definite solution of the nonlinear matrix equation X = Q + LX−1LT , where Q is symmetric positive definite and L is nonsingular. Such equations arise for instance in the analysis of stationary Gaussian reciprocal processes over a finite interval. Its unique largest positive definite solution coincides with the unique positive...

For every symmetric (“palindromic”) word S(A,B) in two positive definite letters and for each fixed n-by-n positive definite B and P , it is shown that the symmetric word equation S(A,B) = P has an n-by-n positive definite solution A. Moreover, if B and P are real, there is a real solution A. The notion of symmetric word is generalized to allow non-integer exponents, with certain limitations. I...

We study numerical methods for finding the maximal symmetric positive definite solution of the nonlinear matrix equation X = Q + LX−1LT , where Q is symmetric positive definite and L is nonsingular. Such equations arise for instance in the analysis of stationary Gaussian reciprocal processes over a finite interval. Its unique largest positive definite solution coincides with the unique positive...