Andrey Chesnokov

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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)
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 squares approximation problem. To compute these polynomials, we pose the inverse eigenvalue problem and solve it efficiently and in a(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 diagonalplus-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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