相关论文: The Voigt and complex error function: Huml\'i\v{c}…
We establish rigorous error bounds for prime counting using a truncated Gaussian (TG) kernel in the explicit formula framework. Our main theorem proves that the approximation error remains globally below 1/2 for all sufficiently large…
The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem…
For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple…
In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one,…
This paper explains how to develop Verilog hardware description language (HDL) optimized flow graph compiled simulators. It is claimed that the methods and algorithms described here can be applied in the development of flow graph compilers…
We propose a new approach to discretize the von Neumann equation, which is efficient in the semi-classical limit. This method is first based on the so called Weyl's variables to address the stiffness associated with the equation. Then, by…
Following recent interest in correctly rounded math library functions (as currently recommended by the IEEE 754 standard), we have designed several SIMD algorithms for one-input single precision functions and integrated them into our CPU…
In previous work, we proposed a method for leveraging efficient classical simulation algorithms to aid in the analysis of large-scale fault tolerant circuits implemented on hypothetical quantum information processors. Here, we extend those…
To well understand the behavior of quantum error correction codes (QECC) in noise processes, we need to obtain explicit coding maps for QECC. Due to extraordinary amount of computational labor that they entails, explicit coding maps are a…
Many randomized approximation algorithms operate by giving a procedure for simulating a random variable $X$ which has mean $\mu$ equal to the target answer, and a relative standard deviation bounded above by a known constant $c$. Examples…
We design new approximation algorithms for the Multiway Cut problem, improving the previously known factor of 1.32388 [Buchbinder et al., 2013]. We proceed in three steps. First, we analyze the rounding scheme of Buchbinder et al., 2013 and…
This paper provides a bound on the number of numeric operations (fixed or floating point) that can safely be performed before accuracy is lost. This work has important implications for control systems with safety-critical software, as these…
When a group acts on a set, it naturally partitions it into orbits, giving rise to orbit problems. These are natural algorithmic problems, as symmetries are central in numerous questions and structures in physics, mathematics, computer…
In this paper, we provise an implementation of five, seven and nine-qubits error correcting codes on a classical computer using the quantum simulator Feynman program. We also compare the three codes by computing the fidelity when double…
Recently a number of randomized 3/4-approximation algorithms for MAX SAT have been proposed that all work in the same way: given a fixed ordering of the variables, the algorithm makes a random assignment to each variable in sequence, in…
An algorithm is presented for approximating arbitrary powers of a black box unitary operation, $\mathcal{U}^t$, where $t$ is a real number, and $\mathcal{U}$ is a black box implementing an unknown unitary. The complexity of this algorithm…
We consider a fractional 0-1 programming problem arising in manufacturing. The problem consists in clustering of machines together with parts processed on these machines into manufacturing cells so that intra-cell processing of parts is…
Finite precision computations using digital computers involve the following inherent errors: (1) Round-off error of finite precision computations (2) Binary computer arithmetic precludes exact number representation of traditional decimal…
Following recent advances in combining approximation algorithms with fixed-parameter tractability (FPT), we study FPT-time approximation algorithms for minimum-norm $k$-clustering problems, parameterized by the number $k$ of open…
Using exact computer arithmetic, it is possible to determine the (exact) solution of a numerical model without rounding error. For such purposes, a corresponding system of equations should be exactly defined, either directly or by…