Nonlinear resonance set for nonlinear matrix equations

✍ Scribed by Caryl Margulies; William Margulies

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 121 KB
• Volume: 293
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(99)00040-3

✦ Synopsis

We study nonlinear matrix equations of the form ex f x, where f is mildly nonlinear. We identify a particular set, called the Fu cik spectrum or resonance set, which is relevant to questions of solvability of the equation. We develop theorems to describe the spectrum and show how it relates to the solvability of the matrix equation. We see that a small perturbation in the constant coecients in f may cause a radical change in the character of the solutions of ex f x.