Synopsis
Explore how to compute a matrix transformation that achieves a desired spectrum, using two practical numerical formulations. Learn how these approaches guide the solution of the additive inverse eigenvalue problem and related tasks.
The material frames the problem around A(c) and a target spectrum, then compares two formulations. It discusses when solutions exist, how to compute them, and how convergence behaves under different eigenvalue structures. The discussion includes the advantages of a Newton-based approach and the challenges of ill-conditioning in practice.
- Two formulations of the inverse eigenvalue problem and when each is appropriate
- How Newton’s method is applied to solve the nonlinear systems that arise
- Differences in convergence for distinct versus multiple eigenvalues
- Practical considerations such as conditioning, cost of forming Jacobians, and numerical behavior
Ideal for readers of numerical linear algebra and inverse problems seeking a solid, applied foundation.
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