Maxentropic interpolation by cubic splines with possibly noisy data

Details Maxentropic interpolation by cubic splines with possibly noisy data Maxentropic interpolation by cubic splines with possibly noisy data

May 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001aipc..568..216g&link_type=abstract

BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: 20th International Workshop. AIP Conference Proceedi

Computer Science

Information Theory

Integral And Integrodifferential Equations, Interpolation, Curve Fitting, Information Theory And Communication Theory

Scientific paper

The gist of this note is to present a procedure for obtaining numerical solutions of Fredholm equations of the first kind of the type ∫01K(s,t)x(t)dt+ɛ(s)=y(s), where K:V-->W is a linear operator mapping V=C([0,1]), the continuous functions on [0, 1], into some other Banach space of functions W, and ɛ is a W-valued random process. The procedure followed consists of partitioning [0, 1] and leaving the values of x(t) at the points of the partitions as unknowns to be found by the method of maximum entropy in the mean. The data vector is also approximated by a finitely dimensional vector, and at the end we obtain an algebraic problem Ax+ɛ=ywhere the matrix A is obtained from the kernel K applied to the cubic spline that approximates x. .

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