Abstract
The total positivity of collocation, Wronskian and Gram matrices corresponding to bases of the form (eλt,teλt,…,tneλt) is analyzed. A bidiagonal decomposition providing the accurate numerical resolution of algebraic linear problems with these matrices is derived. The numerical experimentation confirms the accuracy of the proposed methods.
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Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work was partially supported through the Spanish research grant PGC2018-096321-B-I00 (MCIU/AEI) and by Gobierno de Aragón (E41_20R).
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Communicated by: Lothar Reichel
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Mainar, E., Peña, J.M. & Rubio, B. Accurate computations with matrices related to bases {tieλt}. Adv Comput Math 48, 38 (2022). https://doi.org/10.1007/s10444-022-09954-2
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DOI: https://doi.org/10.1007/s10444-022-09954-2
Keywords
- High relative accuracy
- Bidiagonal decompositions
- Totally positive matrices
- Collocation matrices
- Wronskian matrices
- Gram matrices