Related papers: Series Prediction based on Algebraic Approximants
Matrix functions are a central topic of linear algebra, and problems requiring their numerical approximation appear increasingly often in scientific computing. We review various limited-memory methods for the approximation of the action of…
Difference schemes are considered for dynamical systems $ \dot x = f (x) $ with a quadratic right-hand side, which have $t$-symmetry and are reversible. Reversibility is interpreted in the sense that the Cremona transformation is performed…
This work presents a novel matrix-based method for constructing an approximation Hessian using only function evaluations. The method requires less computational power than interpolation-based methods and is easy to implement in matrix-based…
This work introduces non-Hermitian position-dependent mass Hamiltonians characterized by complex ladder operators and real, equidistant spectra. By imposing the Heisenberg-Weyl algebraic structure as a constraint, we derive the…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
For any power series $a(t)$ with exponentially bounded nonnegative integer coefficients we suggest a simple construction of a finitely generated monomial associative algebra $R$ with Hilbert series $H(R,t)$ very close to $a(t)$. If $a(t)$…
This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…
We introduce concepts of "recursive polynomial remainder sequence (PRS)" and "recursive subresultant," and investigate their properties. In calculating PRS, if there exists the GCD (greatest common divisor) of initial polynomials, we…
Several predictive algorithms are described. Highlighted are variants that make predictions by superposing fields associated to the training data instances. They operate seamlessly with categorical, continuous, and mixed data. Predictive…
We obtain bounds on the average size of Bohr sets with coefficients parametrised by polynomials over finite fields and obtain a series of general results and also some sharper results for specific sets which are important for applications…
We develop an underlying relationship between the theory of rational approximations and that of isomonodromic deformations. We show that a certain duality in Hermite's two approximation problems for functions leads to the Schlesinger…
A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…
We discuss the relation between the linear Tschebyshev-Pad\'e approximations to analytic function $f$ and the diagonal type I Hermite-Pad\'e polynomials for the tuple of functions $[1,f_1,f_2]$ where the pair of functions $f_1,f_2$ forms…
A complete p-adic Khintchine type theorem for approximation by p-adic algebraic numbers is established.
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
This article introduces the R package hermiter which facilitates estimation of univariate and bivariate probability density functions and cumulative distribution functions along with full quantile functions (univariate) and nonparametric…
A compact and accurate solution method is provided for problems whose infinite power series solution diverges and/or whose series coefficients are only known up to a finite order. The method only requires that either the power series…
This paper provides the first criteria for the linear independence of multiple polylogarithm values over algebraic number fields. In particular, we derive novel results regarding the linear independence of products of polylogarithms at…
We present a new algorithm for reconstructing an exact algebraic number from its approximate value using an improved parameterized integer relation construction method. Our result is consistent with the existence of error controlling on…
Properties of certain $q$-orthogonal polynomials are connected to the $q$-oscillator algebra. The Wall and $q$-Laguerre polynomials are shown to arise as matrix elements of $q$-exponentials of the generators in a representation of this…