We compute the inverse of a specific infinite r-dimensional matrix, thus unifying multidimensional matrix inversions recently found by Milne, Lilly, and Bhatnagar. Our inversion is an r-dimensional extension of a matrix inversion previously found by Krattenthaler. We also compute the inverse of another infinite r-dimensional matrix. As applications of our matrix inversions, we derive new summat...

Among offshore hydrocarbon exploration technologies, the controlled source electromagnetic (CSEM) method have gained a lot of interest in both academia and industry because of its ability to detect hydrocarbon reservoirs [1]. In order to maximally extract information from the data, a full nonlinear inversion approach is employed [2]. In such an approach, the investigation domain is subdivided i...

Abstract. We compute the inverse of a specific infinite r-dimensional matrix, thus unifying multidimensional matrix inversions recently found by Milne, Lilly, and Bhatnagar. Our inversion is an r-dimensional extension of a matrix inversion previously found by Krattenthaler. We also compute the inverse of another infinite r-dimensional matrix. As applications of our matrix inversions, we derive ...

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case i r δ > − are discussed. An algorithm that avoids matrix inversion with the case 1 0 i δ − < < is proposed. Keywords—Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion.

thin films of polymer doped with nonlinear optical organic dye, disperse red 1, at thickness of 1 to 2 micrometers, were prepared and studied. in order to induce an axial and orientational alignment of dye molecules within polymer matrix, a contact electric field poling was used. by this process the inherent inversion symmetry in the polymer matrix was eliminated to achieve the desired macrosco...