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In statistics, experimental designs are methods for making efficientexperiments. E-optimal designs are the multisets of experimental conditionswhich minimize the maximum axis of the confidence ellipsoid of estimators. Theaim of this thesis is to propose a new algorithm for constructing E-optimaldesigns approximately for weighted polynomial regression with a nonnegativeweight function.  First, an algorithm to calculate E-optimal designs for weighted polynomialregression of particular weight functions is discussed. Next a new algorithmfor constructing E-optimal designs approximately is proposed. Notions of theTchebycheff systems and orthogonal polynomials are used in the proposedalgorithm. Finally in this thesis, the results of numerical examples are shownin order to verify the accuracy of the E-optimal designs computed by theproposed algorithm.

An Approximate Approach to E-optimal Designs for Weighted Polynomial Regression by Using Tchebycheff Systems and Orthogonal Polynomials