Related papers: Formal power series
This paper focuses on numerical approximation for fractional powers of elliptic operators on $2$-d manifolds. Firstly, parametric finite element method is employed to discretize the original problem. We then approximate fractional powers of…
This paper offers an algorithmic solution to the problem of obtaining "economical" formulae for some maps in Simplicial Topology, having, in principle, a high computational cost in their evaluation. In particular, maps of this kind are used…
We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce…
In many applications (hupergeometric-type) special functions like orthogonal polynomials are needed. For example in more than 50% of the published solutions for the (application-oriented) questions in the "Problems Section" of SIAM Review…
In this paper, we consider formal series associated with events, profiles derived from events, and statistical models that make predictions about events. We prove theorems about realizations for these formal series using the language and…
In this note is presented a method, given nodal values on multidimensional nonconforming spectral elements, for calculating global Fourier-series coefficients. This method is ``exact'' in that given the approximation inherent in the…
In this paper, a formula for the solution of the Poincar\'{e} functional equation in algebra of formal power series and its application to continuous iteration are presented.
In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for…
We discuss and illustrate the behaviour of the continued fraction expansion of a formal power series under specialisation of parameters or their reduction modulo $p$ and sketch some applications of the reduction theorem here proved.
We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra.
We formally verify an algorithm for approximate policy iteration on Factored Markov Decision Processes using the interactive theorem prover Isabelle/HOL. Next, we show how the formalized algorithm can be refined to an executable, verified…
We present an algorithm to construct a basis of k-th extension group of a D-module M in ring of the formal power series Ext_D^k(M,O).
In this article we present a method for formally proving the correctness of the lazy algorithms for computing homographic and quadratic transformations -- of which field operations are special cases-- on a representation of real numbers by…
We propose a general machine learning-based framework for building an accurate and widely-applicable energy functional within the framework of generalized Kohn-Sham density functional theory. To this end, we develop a way of training…
The Fourier spectrum at a fractional period is often examined when extracting features from biological sequences and time series. It reflects the inner information structure of the sequences. A fractional period is not uncommon in time…
Holonomic functions play an essential role in Computer Algebra since they allow the application of many symbolic algorithms. Among all algorithmic attempts to find formulas for power series, the holonomic property remains the most important…
This work presents a new algorithm for matrix power series which is near-sparse, that is, there are a large number of near-zero elements in it. The proposed algorithm uses a filtering technique to improve the sparsity of the matrices…
System identification is a necessity in control theory. Classical control theory usually considers processes with integer order transfer functions. Real processes are usually of fractional order as opposed to the ideal integral order…
In various applications, computers are required to compute approximations to univariate elementary and special functions such as $\exp$ and $\arctan$ to modest accuracy. This paper proposes a new heuristic for automating the design of such…
In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…