The matrix with is therefore an eigenvector matrix for : .Variations Various modifications of the second difference matrix arise and similar results can be derived. For example, consider the matrix obtained by changing the element to : It can be shown that has element and eigenvalues , . If ...
Second order matrix differential equations of the type (1.1) $$AY''(t) + BY'(t) + CY(t) = F(t), a \\\leqq t \\\leqq b$$ where A,B,C,F(t) and Y(t) are pxp complex matrices, elements of C PXP , appear in vibrational systems [12] , in electrical and thermal problem...
I have an NxN matrix 'phi' that is a function of x and y, and is constantly getting updated over iteration (is a function of t as well). To calculate the Laplacian (sum of spatial second derivatives), I calculate the second centred difference, defined as : ...
A space of boundary values is constructed for a minimal symmetric second-order difference operator with matrix coefficients on the whole-line. A description of all maximal dissipative, maximal accretive, self-adjoint and other extensions of such operators is given in terms of boundary conditions at ...
In this paper, we present a generalization of the Hessian matrix toC 1,1 functions, i.e., to functions whose gradient mapping is locally Lipschitz. This type of function arises quite naturally in nonlinear analysis and optimization. First the properties of the generalized Hessian matrix are inves...
My matrix has 80,000 data value with time. So, I have 80,000 rows and 2 columns which are time and data values. Please help me with this. In another way i can explain as, suppose I have a data of ramp input and there are 80,000 point...
When there are N bulk bands below the bandgap, \({\cal F}_{xy}\) is an N × N matrix, whose elements are \({\cal F}_{xy}^{\alpha \beta } = \partial _x{\cal A}_y^{\alpha \beta } - \partial _y{\cal A}_x^{\alpha \beta } + i[ {{\cal A}_x,{\cal A}...
Because of this change in meaning, each value in the matrix no longer represents a probability, but rather a vote. Votes will be summed and compared to determine next word . 由于这种含义的变化,矩阵中的每个值不再代表一个概率,而是一个投票。投票将被汇总并进行比较,以确定下一个单词预测。
where \({{{\boldsymbol{\omega }}}\) and \({{{\bf{k}}}\) are the wave angular frequency and vector, c and \({{{\boldsymbol{I}}}\) are the speed of light and the identity matrix, and \({{{\bf{E}}}\) is the electric field. Note that quantities with subscripts 1 are ...
Secondly, three fast Krylov subspace solvers with suitable circulant preconditioners are designed to solve the discretized linear systems with the Toeplitz matrix. In each iterative step, these methods reduce the memory requirement of the resulting linear equations from $\\\mathcal{O}(N^2)$ to $...