Sturm's Theorem - Generalized Sturm Chains

Generalized Sturm Chains

Let ξ be in the compact interval . A generalized Sturm chain over is a finite sequence of real polynomials (X0,X1,…,Xr) such that:

  1. X(a)X(b) ≠ 0
  2. sign(Xr) is constant on
  3. If Xi(ξ) = 0 for 1 ≤ i ≤ r−1, then Xi−1(ξ)Xi+1(ξ) < 0.

One can check that each Sturm chain is indeed a generalized Sturm chain.

Read more about this topic:  Sturm's Theorem

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