The limitations of SUTCCSP have been addressed in this study due to the loss of the correlation information during the simultaneous diagonalization
process of the covariance and pseudocovariance matrices.
In this paper, we applied a diagonalization
method with nested method of successive averages (MSA) to solve the aforementioned VI problems.
Note that both of the intersection matrices of E and F are negative definite again by diagonalization
of the intersection matrices.
Although the calculation was performed using the FEM in all cases, the spectral scheme that involves the diagonalization
of the Hamiltonian matrix resulting from expansion (6) was also applied and the corresponding results appear superimposed to the FEM ones in Figure 2(a), showing a remarkably good coincidence.
have solved the problem of blind identification of FIR MIMO systems driven by cyclostationary inputs whose cyclic frequencies are pairwise distinct using joint block diagonalization
based on BFGS method in .
VASP code performs an iterative diagonalization
of the Kohn-Sham Hamiltonian via unconstrained band-by-band minimization of the norm of the residual vector to each eigenstate and via optimized charge density mixing routines.
Naturally, as the dimensionality of the matrices becomes very high, i.e., several tens or hundreds of thousands and above, explicit methods of function evaluation, like exact diagonalization
, break down and approximations must be made.
Given N nodes of the ENM, NMA requires a diagonalization
of a 3N x 3N matrix of second derivatives of the potential energy (Hessian matrix), which is performed via eigenanalysis of the Hessian matrix.
Proof: Either analogous to the proofs of Corollary 2.2 and Theorem 3.3 or by a standard diagonalization
The simplest variant is associated with the explicit construction of the solution using the known eigenvalues and eigenfunctions of the elliptic operator with diagonalization
of the corresponding matrix [5,14,15].