The eigenproblem for an n-by-n matrix A is the problem of the approximation (within a relative error bound 2 ?b) of all the eigenvalues of the matrix A and computing the associated eigenspaces of all these eigenvalues. We show that the arithmetic complexity of this problem is bounded by O(n 3 + (n log 2 n) log b). If the characteristic and minimum polynomials of the matrix A coincide with each ...

In Part I, under the bit operation cost model we achieved nearly optimal randomized solution of nonsingular Toeplitz/Hankel linear system of equations based on Hensel's lifting. In Part II, we extend these results to the singular Toeplitz/Hankel-like case based on the MBA divide-and conquer algorithm and its combination with Hensel's lifting. We specify randomization and estimate the error/fail...

The problem of computing an approximate solution of an overdetermined system of linear equations is considered. The usual approach to the problem is least squares, in which the 2-norm of the residual is minimized. This produces the minimum variance unbiased estimator of the solution when the errors in the observations are independent and normally distributed with mean 0 and constant variance. I...

commonly known as Hilbert's matrix, determines a bounded linear operator on the Hilbert space of square summable complex sequences. Infinite matrices which possess a similar form to H, namely those that are 'one way infinite' and have identical entries in cross diagonals, are called Hankel matrices, and when these matrices determine bounded operators we have Hankel operators, the subject of thi...

We apply and extend some well known and some recent techniques from algebraic residue theory in order to relate to each other two major subjects of algebraic and numerical computing that is computations with structured matrices and solving a system of polynomial equations In the rst part of our paper we extend the Toeplitz and Hankel structures of matrices and some of their known properties to ...

whenever Φ is such that this extends to a bounded operator on Lpr0, asq. Whenever a is of no importance we will omit it from the notation. We abbreviate by saying that WΦ is a TWH-operator. These operators (or rather, unitarily equivalent ones) also go under the name finite interval convolution operators, truncated Hankel operators or Toeplitz operators on the Paley-Wiener space. See e.g. [1, 2...

‎the objective of this paper is to obtain an upper bound to the second hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$‎ ‎for the function $f$‎, ‎belonging to the class of gamma-starlike functions‎, ‎using toeplitz determinants‎. ‎the result presented here include‎ ‎two known results as their special cases‎.