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...Curve fitting using least square principle p sam johnson february nit karnataka overview the study of approximation theory involves two general types problems one problem arises when a function is given explicitly but we wish to nd simpler type such as polynomial that can be used determine approximate values taylor degree n about number x an excellent times dierentiable f in small neighbourhood second concerned with tting functions data and best certain class represent lagrange interpolating polynomials are approximating they t limitations these techniques considerd other avenues approach discussed lecture introduction many branches applied mathematics engineering sciences come across experiments which involve variables for example it known speed v ship varies horse power engine according formula bv here b constants determined this purpose take several sets readings speeds corresponding powers thus suitable relation or law may exist between y from set observed xi yi i connecting empiri...