A computable error bound for matrix functionals

A Computable Error Bound for Matrix Functionals

Many problems in applied mathematics require the evaluation of matrix functionals of the form F(A) := u T f(A)u, where A is a large symmetric matrix and u is a vector. Golub and collaborators have described how approximations of such functionals can be computed inexpensively by using the Lanczos algorithm. The present note shows that error bounds for these approximations can be computed essenti...

Towards an arithmetic for partial computable functionals

• It is unlikely that there is an algorithm f that decides (1), i.e., returns tt if x = 0 and ff if x 6= 0: on input x = 0 it would run forever (think of the decimal representation of x); it would only semi-decide it, i.e., it would be a partial algorithm. • The algorithm as a mapping f : R→ B is discontinuous at 0. • Reals are Cauchy sequences of rationals; rationals are pairs of integers; int...

The basic feasible functionals in computable analysis

We give a correspondence between two notions of complexity for real numbers and functions: poly-time computability according to Ko and a notion that arises naturally when one considers the application of Melhorn’s class of the Basic Feasible Functionals to computable analysis. We show that both notions define the same set of real numbers and functions.

Parallel computable higher type functionals (Extended Abstract)

A bound for Feichtinger conjecture

In this paper‎, ‎using the discrete Fourier transform in the finite-dimensional Hilbert space C^n‎, ‎a class of nonRieszable equal norm tight frames is introduced ‎and‎ using this class, a bound for Fiechtinger Conjecture is presented. By the Fiechtinger Conjecture that has been proved recently, for given A,C>0 there exists a universal constant delta>0 independent of $n$ such that every C-equal...