β Scribed by Sidi Mahmoud Ould Kaber
No coin nor oath required. For personal study only.
We consider a non-periodic function u with Legendre expansion Eke, 0 ~L k. The best approximation of u, in the L 2 sense, by N N-degree polynomials is the truncated series ~rNu = E~. 0 ~kLk. When the function u is discontinuous, the polynomial approximation rrNu is oscillatory. We present a filter that acts on ~rNu to give a good approximation of u.
π SIMILAR VOLUMES
A result of Godambe [1] on optimal combination of estimating functions for discrete time stochastic processes is extended to discrete time state space models and to continuous time counting process models. The extensions so obtained may be applicable in a wider context than the standard notions base
An algorithm is given for the computer evaluation of polyspheroidal periodic functions and their eigenvalues for different values of the parameters v, II, g, n, z. The eigenvalues are found by minimization of n times folded continued fractions. The eigenfunctions are evaluated by summation of the ap