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A fast solution algorithm is proposed for solving block banded block Toeplitz systems with non-banded Toeplitz blocks. The algorithm constructs the circulant transformation of a given Toeplitz system and then by means of the Sherman-Morrison-Woodbury formula transforms its inverse to an inverse of the original matrix. The block circulant matrix with… (More)

A method to compute recurrence relation coefficients for bivariate orthogonal polynomials by unitary matrix transformations Abstract We present an algorithm computing recurrence relation coefficients for bivariate polynomials, orthonormal with respect to a discrete inner product. These polynomials make it possible to give the solution of a discrete least… (More)

A numerical algorithm is presented to solve the constrained weighted energy problem from potential theory. As one of the possible applications of this algorithm , we study the convergence properties of the rational Lanczos iteration method for the symmetric eigenvalue problem. The constrained weighted energy problem characterizes the region containing those… (More)

A dense symmetric matrix can be reduced into a similar diagonal-plus-semiseparable one by means of orthogonal similarity transformations. This makes such a diagonal-plus-semiseparable representation a good alternative to the tridiagonal one when solving dense linear algebra problems. For symmetric tridiagonal matrices there have been developed different… (More)

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