Abstract
The algebraic Riccati matrix equation is used for eigendecomposition of special structured matrices. This is achieved by similarity transformation and then using the algebraic Riccati matrix equation to the triangulation of matrices. The process is the decomposition of matrices into small and specially structured submatrices with low dimensions for easy finding of eigenpairs. Here, we show that previous canonical forms I, II, III, and so on are special cases of the presented method. Numerical and structural examples are included to show the efficiency of the present method.
Highlights
Eigenvalue problem is a special category for studying of engineering problems
We introduce a general solution form of canonical and symmetry forms I, II, III, and so on which presented in [8,9,10, 29,30,31,32,33,34]
The solution can be obtained by solving the algebraic Riccati equation when X = I
Summary
Eigenvalue problem is a special category for studying of engineering problems. As an example, the eigenvalues correspond to natural frequencies in vibration of systems and buckling loads in the stability analysis of structures [1,2,3,4]. A review of application and solution of the algebraic Riccati matrix equation can be found in [27, 28]. We introduce a general solution form of canonical and symmetry forms I, II, III, and so on which presented in [8,9,10, 29,30,31,32,33,34]. This is achieved via using similarity transformations and the solutions of the algebraic Riccati matrix equation
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