Discrete Lanczos derivatives of noisy data. (English) Zbl 1259.65051
Summary: Finite differences are frequently used to differentiate empirical functions, but standard differences tend to amplify the random error that is present in almost all empirical data. This paper uses higher-order Lanczos derivatives and discretized Legendre polynomials to generate minimum variance finite differences to approximate ordinary derivatives of all orders for a fixed discretization error magnitude. The resulting differences can be implemented as finite impulse response filters and are therefore very fast on a computer.
MSC:
| 65D25 | Numerical differentiation |
Keywords:
Lanczos derivative; differentiator; least squares; Legendre polynomial; numerical differentiation; numerical examplesReferences:
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