Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
Constructive Approximation of Nonlinear Operators Based on Piecewise Interpolation Technique. |
| Συγγραφείς: |
Torokhti, Anatoli1 (AUTHOR) anatoli.torokhti@gmail.com, Pudney, Peter1 (AUTHOR) |
| Πηγή: |
Axioms (2075-1680). Feb2026, Vol. 15 Issue 2, p91. 25p. |
| Θεματικοί όροι: |
*Nonlinear operators, *Interpolation, *Operator theory, *Approximation theory, *Pseudoinverses, *Mathematical analysis, *Lipschitz continuity, *Random variables |
| Περίληψη: |
Suppose K Y and K X are the image and the preimage of a nonlinear operator F : K Y → K X . It is supposed that the cardinality of each K Y and K X is N and N is large. We provide an approximation to the map F that requires prior information only on a few elements p from K Y , where p ≪ N , but still effectively represents F (K Y) . It is achieved under Lipschitz continuity assumptions. The device behind the proposed method is based on a special extension of the piecewise linear interpolation technique to the case of sets of stochastic elements. The proposed technique provides a single operator that transforms any element from the arbitrarily large set K Y . The operator is determined in terms of pseudo-inverse matrices so that it always exists. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: |
Academic Search Index |