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:
- X(a)X(b) ≠ 0
- sign(Xr) is constant on
- 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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