Different numerical techniques for the solution of transcendental eigenvalue problem in transmission line bundles

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Numerical solution of a quadratic eigenvalue problem

We consider the quadratic eigenvalue problem (QEP) (λ2M + λG + K)x = 0, where M = MT is positive definite, K = KT is negative definite, and G = −GT . The eigenvalues of the QEP occur in quadruplets (λ, λ,−λ,−λ) or in real or purely imaginary pairs (λ,−λ). We show that all eigenvalues of the QEP can be found efficiently and with the correct symmetry, by finding a proper solvent X of the matrix e...

Progress in the numerical solution of the nonsymmetric eigenvalue problem

Having worked several years on the LAPACK project [2] and having communicated with a variety of users who work in diverse fields involving scientific computing, the author has seen a growing demand for the numerical solution of the eigenvalue problems. Since the publication of Parlett’s exploratory review paper, ‘The software scene in the extraction of eigenvalues from sparse matrices’ [35], ne...

The Transmission Eigenvalue Problem

This paper provides a survey of recent developments on the transmission eigenvalue problem.

The Transcendental Eigenvalue Problem and Its Application in System Identification