Rank-Structured QR for Chebyshev Rootfinding

Casulli, Angelo; Robol, Leonardo

doi:10.1137/20m1375115

SIAM J. Matrix Anal. Appl.

2021

DOI: 10.1137/20m1375115

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Rank-Structured QR for Chebyshev Rootfinding

Angelo Casulli¹,

Leonardo Robol²

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2023

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Revisiting the computation of the critical points of the Keplerian distance

Gronchi,

Baù,

Grassi

2023

Celest Mech Dyn Astron

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We consider the Keplerian distance d in the case of two elliptic orbits, i.e., the distance between one point on the first ellipse and one point on the second one, assuming they have a common focus. The absolute minimum $$d_{\textrm{min}}$$ d min of this function, called MOID or orbit distance in the literature, is relevant to detect possible impacts between two objects following approximately these elliptic trajectories. We revisit and compare two different approaches to compute the critical points of $$d^2$$ d 2 , where we squared the distance d to include crossing points among the critical ones. One approach uses trigonometric polynomials, and the other uses ordinary polynomials. A new way to test the reliability of the computation of $$d_{\textrm{min}}$$ d min is introduced, based on optimal estimates that can be found in the literature. The planar case is also discussed: in this case, we present an estimate for the maximal number of critical points of $$d^2$$ d 2 , together with a conjecture supported by numerical tests.

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Revisiting the computation of the critical points of the Keplerian distance

Gronchi,

Baù,

Grassi

2023

Celest Mech Dyn Astron

View full text Add to dashboard Cite

show abstract

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Rank-Structured QR for Chebyshev Rootfinding

Cited by 1 publication

References 20 publications

Revisiting the computation of the critical points of the Keplerian distance

Revisiting the computation of the critical points of the Keplerian distance

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