Eigenvalue localization for the tikhonova model of crystal growth

✍ Scribed by Charlie H. Cooke; Philip W. Smith

• Book ID: 103084634
• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 356 KB
• Volume: 316
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(83)90081-9

✦ Synopsis

Matrix A with characteristic polynomial Q(z) is defined positive or negative Hurwitz according to whether Q(z) or Q(-z) is a Hurwitz polynomial. Leading principle sections of the Tikhonova growth matrix have associated characteristic polynomials P"( -z) which satisfy the recursion p,+ l(Z) = zP,(z) + 1 ----Pp,_,(z), P,(z) = 1, PI(Z) = 1 +z. n(n + 1) That the Tikhonova growth matrix is negative Hurwitz is established through applying the Wall-Stieltjes theory of continued fraction expansions to show the P,(z) are Hurwitz polynomials. The Kayeya-Enestrom theorem and a procedurefor refinement of the Gerschgorin estimate are used to obtain analytical bounds on spectral radii for the Tikhonova model, which provides estimates of maximal growth rates. The theory allows generalization to more complicated growth models. '. 1 '.