An iterative algorithm is given for solving a system Ax = k of n linear equations in n unknowns. The solution is given in n steps . It is shown that this m ethod is a special case of a very general m et hod which also includes Gaussian elimination . Th ese general algorithms are essentially algorithms for findin g an n dimensional ellipsoid . Connections a re m a de wit h the theo ry of orthogonal p olynomials and continued fractions.

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