TY - GEN
T1 - Optimal Node Placement for Constrained Polynomial Interpolation
AU - Ninevski, Dimitar
AU - O'Leary, Paul
AU - Terbuch, Anika
AU - Harker, Matthew
N1 - Publisher Copyright:
© 2025 IEEE.
PY - 2025
Y1 - 2025
N2 - In this paper, an algorithm for optimizing the Lebesgue constant of a set of nodes is demonstrated. First, the standard Lebesgue function and Lebesgue constant are used to show how the location of the nodes affect the interpolating qualities of a set of polynomials. Next, the definition of the Lebesgue function and constant is generalized to any set of polynomials, including constrained polynomials. To that end, an algorithm is developed for optimizing a set of nodes by indirectly minimizing the Lebesgue constant. Finally, the performance of the algorithm is shown on several examples, including one with a known theoretical solution and a boundary value problem. The optimal nodes obtained via the algorithm can then be used for generating admissible polynomials for hybrid machine learning which have good interpolating and approximating qualities.
AB - In this paper, an algorithm for optimizing the Lebesgue constant of a set of nodes is demonstrated. First, the standard Lebesgue function and Lebesgue constant are used to show how the location of the nodes affect the interpolating qualities of a set of polynomials. Next, the definition of the Lebesgue function and constant is generalized to any set of polynomials, including constrained polynomials. To that end, an algorithm is developed for optimizing a set of nodes by indirectly minimizing the Lebesgue constant. Finally, the performance of the algorithm is shown on several examples, including one with a known theoretical solution and a boundary value problem. The optimal nodes obtained via the algorithm can then be used for generating admissible polynomials for hybrid machine learning which have good interpolating and approximating qualities.
KW - Lebesgue constant
KW - Lebesgue function
KW - Node placement
KW - admissible functions
KW - hybrid machine learning
UR - https://www.scopus.com/pages/publications/105010470253
U2 - 10.1109/MECO66322.2025.11049123
DO - 10.1109/MECO66322.2025.11049123
M3 - Contribution to conference proceedings
AN - SCOPUS:105010470253
T3 - 2025 14th Mediterranean Conference on Embedded Computing, MECO 2025 - Proceedings
BT - 2025 14th Mediterranean Conference on Embedded Computing, MECO 2025 - Proceedings
A2 - Stojanovic, Radovan
A2 - Jozwiak, Lech
A2 - Lutovac, Budimir
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 14th Mediterranean Conference on Embedded Computing, MECO 2025
Y2 - 10 June 2025 through 14 June 2025
ER -