## Abstract

Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introduce an algorithm that produces a tight frame in a finite number of steps. Additionally, we give sharp bounds on additive perturbations which preserve frames and we study the effect of appending and erasing vectors to a given tight frame. We also discuss under which conditions our finite-dimensional results are extendable to infinite-dimensional Hilbert spaces.

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### Topics from this Paper

- Finite Dimensional Hilbert Space
- Tight Frame
- Frame In Space
- Finite Dimensional Space
- Finite Space + Show 5 more

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