Speeding Up a Numerical Algorithm

This paper discusses a numerical task which seems hopeless in terms of resource re- quirements. Transforming it to an equivalent formulation yields an almost two-fold increase in the number of arithmetic operations that are involved. However, this makes the problem computationally feasible. Sounds unbelievable? If you think so, you may want to read further.
A one-dimensional integral transform of the function ƒ with kemel K is defined here as the function F, satisfying F(x) = K(x, y) f(y) dy, for x = [a, b]. Numeri- cal approximations of such integral transforms are important in many scientific and en- gineering problems, and often present a formidable task in terms of computational time and storage requirements. This paper proposes an elementary presentation of some of the difficulties related to computing integral transforms, and a possible remedy.