Synopsis
Solve inverse eigenvalue problems with clear, practical Newton methods.
Learn how to adjust a matrix so it carries a prescribed spectrum, and see how two natural formulations guide numerical solution.
This guide focuses on the additive inverse eigenvalue problem and its two formulations, revealing why one approach often converges faster. It also discusses when solutions exist, how uniqueness plays a role, and what numerical choices matter for stability and efficiency.
- Two formulations of the nonlinear problem and how they differ in conditioning and convergence
- How Newton’s method is applied to each formulation and why one is typically preferred
- Conditions that guarantee quadratic convergence, including cases with distinct or multiple eigenvalues
- Practical considerations for computation, including Jacobian structure and potential pitfalls
Ideal for readers of numerical linear algebra and researchers solving inverse eigenvalue problems in applied contexts.
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