Improved condition number for spectral methods

Source abstract

For the known spectral methods (Galerkin, Tau, Collocation) the condition number behaves like O ( N 4 ) O({N^4}) ( N : maximal degree of polynomials). We introduce a spectral method with an O ( N 2 ) O({N^2}) condition number. The advantages with respect to propagation of rounding errors and preconditioning are demonstrated. A direct solver for constant coefficient problems is given. Extensions to variable coefficient problems and first-order problems are discussed. Numerical results are presented, showing the effectiveness of our methods.