An imbedding method for matrix eigenvalue problems
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In this article, the problem of determining the complex eigenvalues of a general square matrix is reduced to integration in the complex plane of ordinary differential equations subject to known initial conditions, and some formulae from the theory of functions of a complex variable play a crucial role.Abstract:
Determination of the (possibly complex) eigenvalues of a general square matrix is reduced to integration in the complex plane of ordinary differential equations subject to known initial conditions. Some formulae from the theory of functions of a complex variable play a crucial role. The method is illustrated with results of some numerical experiments.read more
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Complete eigen-solutions for plane notches with multi-materials by the imbedding method
Yongjun Xu,Si Yuan +1 more
TL;DR: A robust algorithm is proposed to compute accurate and complete eigen-solutions for plane cracks/notches with multi-materials, arbitrary opening angles and different surface conditions using the general-purpose Ordinary Differential Equation solver COLSYS.
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Analytical aspects of computational linear algebra
Robert E. Kalaba,Nima Rasakhoo +1 more
TL;DR: In this article, the authors deal with a system of ordinary differential equations with known initial conditions associated with a given square matrix, by using standard analytical and computational methods many of the important aspects of the given matrix can be determined.
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