An introduction to inverse algebraic eigenvalue problems (Q2785515)

This is a monograph on mathematical theory and numerical algorithms for inverse algebraic eigenvalue problems. Four interesting special cases are treated in detail: NEWLINENEWLINENEWLINE1. Find a tridiagonal matrix with given spectrum. Conditions for solvability and sensitivity of solution is studied, Lanczos and Householder type algorithms are described.NEWLINENEWLINENEWLINE 2. Pole assignment from control theory. Schur algorithms, invariant subspace algorithm and QR with assigned shifts. These three algorithms are compared on 3 different numerical test examples, and each of them is the most accurate for one of the examples. It is described how to handle complex eigenvalues in real arithmetic, and how to get solutions of smaller norm for multiple input multiple output systems. NEWLINENEWLINENEWLINE3. Additive and multiplicative inverse eigenproblems. Solvability, sensitivity, Newton and homotopy algorithms. NEWLINENEWLINENEWLINE4. Nonnegative matrices. Conditions for solution, minimal spectral radius. NEWLINENEWLINENEWLINEThe bibliography refers to 245 works and is rather exhaustive on recent numerical analysis works in the area.