On Condition Numbers and the Distance to the Nearest Ill-Posed Problem (Classic Reprint): December 1985: December 1985 (Classic Reprint) - Softcover

Inhaltsangabe

Explore how small changes near ill-posed problems reveal big shifts in stability across core numerical tasks. This work shows a unifying view of condition numbers and distance to the nearest ill-posed problem, with concrete links to matrix inversion, eigenvalue computations, polynomial zeros, and pole assignment in control systems.

In clear terms, the book explains how the reciprocal of a condition number bounds how far a problem is from becoming ill-posed. It uses locally available information to answer a global question: how close is the nearest ill-posed case in several important problem classes? The discussion includes differential inequalities, explicit bounds, and practical implications for common numerical tasks, organized to let readers explore each topic independently.

- See how a problem’s sensitivity relates to its distance from ill-posedness.
- Learn the differential-inequality approach and how it yields upper and lower distance bounds.
- Compare results across matrix inversion, eigensystems, polynomial roots, and pole assignment.
- Understand the role of norms and gradients in deriving robust estimates.

Ideal for readers of advanced linear algebra and numerical analysis who want a cohesive framework for stability and conditioning in key computational problems, presented with accessible math and usable insights.

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