Related papers: Computing Borcherds Products
We present the first polynomial time algorithm for computing Walrasian equilibrium in an economy with indivisible goods and \emph{general} buyer valuations having only access to an \emph{aggregate demand oracle}, i.e., an oracle that given…
We introduce an approximation strategy for the discounted moments of a stochastic process that can, for a large class of problems, approximate the true moments. These moments appear in pricing formulas of financial products such as bonds…
This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…
We show that multiplication can be done in polynomial time on a three counter machine that receives its input as the contents of two counters. The technique is generalized to functions of two variables computable by deterministic Turing…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
Let $K$ be a field. Let $f\in K[[x_{1},...,x_{r}]]$ and $g\in K[[y_{1},...,y_{s}]]$ be nonzero elements. If $X$ (resp. $Y$) is a matrix factorization of $f$ (resp. $g$), Yoshino had constructed a tensor product (of matrix factorizations)…
We present algorithms and heuristics to compute the characteristic polynomial of a matrix given its minimal polynomial. The matrix is represented as a black-box, i.e., by a function to compute its matrix-vector product. The methods apply to…
In this paper, we study the arithmetics of skew polynomial rings over finite fields, mostly from an algorithmic point of view. We give various algorithms for fast multiplication, division and extended Euclidean division. We give a precise…
We study the problem of factoring univariate polynomials over finite fields. Under the assumption of the Extended Riemann Hypothesis (ERH), (Gao, 2001) designed a polynomial time algorithm that fails to factor only if the input polynomial…
A method of calculating probability values from a system of marginal constraints is presented. Previous systems for finding the probability of a single attribute have either made an independence assumption concerning the evidence or have…
This paper describes a novel method for efficiently calculating CRC checksums without lookup tables or hardware support for polynomial multiplication. Throughput of CRC32 is increased by 100% across different platforms compared with the…
A syntactical proof is given that all functions definable in a certain affine linear typed lambda-calculus with iteration in all types are polynomial time computable. The proof provides explicit polynomial bounds that can easily be…
The solution of a (stochastic) differential equation can be locally approximated by a (stochastic) expansion. If the vector field of the differential equation is a polynomial, the corresponding expansion is a linear combination of iterated…
IIn computational geometry, the construction of essential primitives like convex hulls, Voronoi diagrams and Delaunay triangulations require the evaluation of the signs of determinants, which are sums of products. The same signs are needed…
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…
We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…
We derive a product formula for the multiple stochastic integrals with respect to Levy process. The idea is to use exponential vectors and the polarization technique which greatly simplify the argument.
We present a probabilistic algorithm to compute the product of two univariate sparse polynomials over a field with a number of bit operations that is quasi-linear in the size of the input and the output. Our algorithm works for any field of…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
Let $C$ be an arithmetic circuit of $poly(n)$ size given as input that computes a polynomial $f\in\mathbb{F}[X]$, where $X=\{x_1,x_2,\ldots,x_n\}$ and $\mathbb{F}$ is any field where the field arithmetic can be performed efficiently. We…