LAUSR

The RAFU (radical functions ) method can be used to obtain the uniform reconstruction of a continuous function from its values at some of the points of partitions of a closed interval . In this work we will prove that we can reconstruct a continuous function from average samples of these points , from linear combinations of them and from local average samples given by convolution . Uniform error bounds will be established . If these data are unknown but approximate values of them are known, uniform reconstruction will be also possible . Error estimates in these cases will be given. The case of a non-uniform net will be treated . Examples and algorithms will be also shown .