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Mixed-precision finite element kernels and assembly: Rounding error analysis and hardware acceleration

Croci, M.; Wells, G. N. (2024-10-16)

In this paper we develop the first fine-grained rounding error analysis of finite element (FE) cell kernels and assembly. The theory includes mixed-precision implementations and accounts for hardware-acceleration via matrix ...

WEIGHTED LORENTZ SPACES: SHARP MIXED Ap − A∞ ESTIMATE FOR MAXIMAL FUNCTIONS

Accomazzo, N.; Duoandikoetxea, J.; Nieraeth, Z.; Ombrosi, S.; Pérez, C. (2023-01-01)

We prove the sharp mixed Ap − A∞ weighted estimate for the Hardy-Littlewood maximal function in the context of weighted Lorentz spaces, namely 11 ∥M∥ p,q ≲p,q,n [w]p [σ]min(p,q) , L (w) Ap A∞ 1 where σ = w 1−p . Our met...

SELF-IMPROVING POINCARE ́-SOBOLEV TYPE FUNCTIONALS IN PRODUCT SPACES

Pérez, C.; Cejas, M.E.; Mosquera, C.; Rela, E. (2021-01-01)

In this paper we give a geometric condition which ensures that (q,p)-Poincar ́e-Sobolev inequalities are implied from generalized (1, 1)-Poincar ́e inequalities related to L1 norms in the context of product spaces. The conce...

AN EXTREMAL PROBLEM AND INEQUALITIES FOR ENTIRE FUNCTIONS OF EXPONENTIAL TYPE

Sousa, M.; Chirre, A.; Dimitrov, D.K.; Quesada-Herrera, E. (2024-01-01)

We study two variations of the classical one-delta problem for entire functions of exponential type, known also as the Carath ́eodory–Fej ́er– Tura ́n problem. The first variation imposes the additional requirement that the ...