scholarly journals Derivative Uniform Sampling via Weierstrass σ(z). Truncation Error Analysis in

2001 ◽  
Vol 8 (1) ◽  
pp. 129-134
Author(s):  
Tibor K. Pogány
Keyword(s):  
Initial Function ◽  
Truncation Error ◽  
Entire Functions ◽  
Third Order ◽  
Reconstruction Procedure ◽  
Sampling Function ◽  
Von Neumann ◽  
Uniform Sampling ◽  
Sampling Series ◽  
Derivative Sampling

Abstract In the entire functions space consisting of at most second order functions such that their type is less than πq/(2s 2) it is valid the q-order derivative sampling series reconstruction procedure, reading at the von Neumann lattice {s(m + ni)| (m, n) ∈ } via the Weierstrass σ(·) as the sampling function, s > 0. The uniform convergence of the sampling sums to the initial function is proved by the circular truncation error upper bound, especially derived for this reconstruction procedure. Finally, the explicit second and third order sampling formulæ are given.

scholarly journals High-order compact LOD methods for solving high-dimensional advection equations

2021 ◽  
Vol 40 (3) ◽  
Author(s):  
Bo Hou ◽  
Yongbin Ge
Keyword(s):  
Truncation Error ◽  
Three Dimensional ◽  
Taylor Series Expansion ◽  
High Order ◽  
High Dimensional ◽  
Analysis Method ◽  
Order Accuracy ◽  
Von Neumann ◽  
One Dimensional ◽  
Von Neumann Analysis

AbstractIn this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for the third derivatives in the truncation error remainder, two high-order compact LOD schemes are established for solving the two- and three- dimensional advection equations, respectively. They have the fourth-order accuracy in both time and space. By the von Neumann analysis method, it shows that the two schemes are unconditionally stable. Besides, the consistency and convergence of them are also proved. Finally, numerical experiments are given to confirm the accuracy and efficiency of the present schemes.

scholarly journals Lattice-Based Linearly Homomorphic Signature Scheme over F 2

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Jie Cai ◽  
Han Jiang ◽  
Hao Wang ◽  
Qiuliang Xu
Keyword(s):  
Public Key ◽  
Side Channel ◽  
Signature Scheme ◽  
Side Channel Attacks ◽  
Sampling Function ◽  
Uniform Sampling ◽  
Restricted Condition ◽  
Gaussian Sampling

In this paper, we design a new lattice-based linearly homomorphic signature scheme over F 2 . The existing schemes are all constructed based on hash-and-sign lattice-based signature framework, where the implementation of preimage sampling function is Gaussian sampling, and the use of trapdoor basis needs a larger dimension m ≥ 5 n   log   q . Hence, they cannot resist potential side-channel attacks and have larger sizes of public key and signature. Under Fiat–Shamir with aborting signature framework and general SIS problem restricted condition m ≥ n   log   q , we use uniform sampling of filtering technology to design the scheme, and then, our scheme has a smaller public key size and signature size than the existing schemes and it can resist side-channel attacks.

Optimal Third-Order Symplectic Integration Modeling of Seismic Acoustic Wave Propagation

2020 ◽  
Vol 110 (2) ◽  
pp. 754-762 ◽  
Author(s):  
Chuan Li ◽  
Jianxin Liu ◽  
Bo Chen ◽  
Ya Sun
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Acoustic Wave ◽  
Seismic Wave ◽  
Truncation Error ◽  
Seismic Wave Propagation ◽  
Symplectic Integrator ◽  
Third Order ◽  
The Third ◽  
2D And 3D

ABSTRACT Seismic wavefield modeling based on the wave equation is widely used in understanding and predicting the dynamic and kinematic characteristics of seismic wave propagation through media. This article presents an optimal numerical solution for the seismic acoustic wave equation in a Hamiltonian system based on the third-order symplectic integrator method. The least absolute truncation error analysis method is used to determine the optimal coefficients. The analysis of the third-order symplectic integrator shows that the proposed scheme exhibits high stability and minimal truncation error. To illustrate the accuracy of the algorithm, we compare the numerical solutions generated by the proposed method with the theoretical analysis solution for 2D and 3D seismic wave propagation tests. The results show that the proposed method reduced the phase error to the eighth-order magnitude accuracy relative to the exact solution. These simulations also demonstrated that the proposed third-order symplectic method can minimize numerical dispersion and preserve the waveforms during the simulation. In addition, comparing different central frequencies of the source and grid spaces (90, 60, and 20 m) for simulation of seismic wave propagation in 2D and 3D models using symplectic and nearly analytic discretization methods, we deduce that the suitable grid spaces are roughly equivalent to between one-fourth and one-fifth of the wavelength, which can provide a good compromise between accuracy and computational cost.

scholarly journals ID-Based Strong Designated Verifier Signature over R-SIS Assumption

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Jie Cai ◽  
Han Jiang ◽  
Pingyuan Zhang ◽  
Zhihua Zheng ◽  
Hao Wang ◽  
...  
Keyword(s):  
Random Model ◽  
Side Channel ◽  
Complex Structures ◽  
Rejection Sampling ◽  
Side Channel Attacks ◽  
Sampling Function ◽  
Uniform Sampling ◽  
Image Sampling ◽  
Designated Verifier ◽  
Designated Verifier Signature

In this paper, we propose an ID-based strong designated verifier signature (SDVS) over R-SIS assumption in the random model. We remove pre-image sampling function and Bonsai trees such complex structures used in previous lattice-based SDVS schemes. We only utilize simple rejection sampling to protect the security of our scheme. Hence, we will show our design has the shortest signature size comparing with existing lattice-based ID-based SDVS schemes. In addition, our scheme satisfies anonymity (privacy of signer’s identity) proved in existing schemes rarely, and it can resist side-channel attacks with uniform sampling.

scholarly journals A quantum algorithm for uniform sampling of models of propositional logic based on quantum probability

2016 ◽  
Vol 16 (1) ◽  
pp. 57-65
Author(s):  
Radhakrishnan Balu ◽  
Dale Shires ◽  
Raju Namburu
Keyword(s):  
Fixed Points ◽  
Propositional Logic ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Probability ◽  
Stochastic Flows ◽  
Von Neumann ◽  
Uniform Sampling ◽  
Successful Technique ◽  
D Wave

We describe a class of quantum algorithms to generate models of propositional logic with equal probability. We consider quantum stochastic flows that are the quantum analogues of classical Markov chains and establish a relation between fixed points on the two flows. We construct chains inspired by von Neumann algorithms using uniform measures as fixed points to construct the corresponding irreversible quantum stochastic flows. We formulate sampling models of propositions in the framework of adiabatic quantum computing and solve the underlying satisfiability instances. Satisfiability formulation is an important and successful technique in modeling the decision theoretic problems in a classical context. We discuss some features of the proposed algorithms tested on an existing quantum annealer D-Wave II extending the simulation of decision theoretic problems to a quantum context.

scholarly journals Accuracy analysis and improvement for the cell-centered scheme with the quasi-one-dimensional reconstriction

2021 ◽  
pp. 1-32 ◽  
Author(s):  
Pavel Alexeevisch Bakhvalov
Keyword(s):  
Transport Equation ◽  
Finite Volume ◽  
Constant Velocity ◽  
Truncation Error ◽  
Finite Volume Scheme ◽  
Accuracy Analysis ◽  
Third Order ◽  
One Dimensional ◽  
The Third ◽  
Dimensional Reconstruction

We study the cell-centered finite-volume scheme with the quasi-one-dimensional reconstruction. For the model transport equation with a constant velocity, we prove that on translationally-invariant (TI) triangular meshes it possesses the second order of the truncation error and, if the solution is steady, the third order of the solution error. We offer the modification possessing the third order of the solution error on TI-meshes for unsteady solutions also and verify its accuracy on unstructured meshes.

Reconstruction of Entire Functions From Irregularly Spaced Sample Points

1996 ◽  
Vol 48 (4) ◽  
pp. 777-793 ◽  
Author(s):  
Georgi R. Grozev ◽  
Qazi I. Rahman
Keyword(s):  
Entire Functions ◽  
Constant Independent ◽  
Real Numbers ◽  
Several Variables ◽  
Derivative Sampling ◽  
Sample Points

AbstractLet where {λn}n ∈ Ζ is a sequence of real numbers such that |λn — n| ≤ Δ for some Δ > 0 and all n ∈ ℤ . Extending an obvious property of sin πz to which the function G reduces when Δ = 0 we show that is bounded by a constant independent of n. The result is then applied to a problem concerning derivative sampling in one and several variables.

scholarly journals New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Norazak Senu ◽  
Mohamed Suleiman ◽  
Fudziah Ismail ◽  
Norihan Md Arifin
Keyword(s):  
Differential Equations ◽  
Truncation Error ◽  
Second Order ◽  
Phase Lag ◽  
Initial Value ◽  
Third Order ◽  
Second Order Differential Equations ◽  
New Methods ◽  
Oscillating Solutions ◽  
Runge Kutta

New 4(3) pairs Diagonally Implicit Runge-Kutta-Nyström (DIRKN) methods with reduced phase-lag are developed for the integration of initial value problems for second-order ordinary differential equations possessing oscillating solutions. Two DIRKN pairs which are three- and four-stage with high order of dispersion embedded with the third-order formula for the estimation of the local truncation error. These new methods are more efficient when compared with current methods of similar type and with the L-stable Runge-Kutta pair derived by Butcher and Chen (2000) for the numerical integration of second-order differential equations with periodic solutions.

A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids

2012 ◽  
Vol 12 (5) ◽  
pp. 1495-1519 ◽  
Author(s):  
Hong Luo ◽  
Luqing Luo ◽  
Robert Nourgaliev
Keyword(s):  
Galerkin Method ◽  
Euler Equations ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Least Squares Method ◽  
Polynomial Solution ◽  
Third Order ◽  
Von Neumann ◽  
Flow Problems ◽  
Dg Method

AbstractA reconstruction-based discontinuous Galerkin (RDG(P1P2)) method, a variant of P1P2 method, is presented for the solution of the compressible Euler equations on arbitrary grids. In this method, an in-cell reconstruction, designed to enhance the accuracy of the discontinuous Galerkin method, is used to obtain a quadratic polynomial solution (P2) from the underlying linear polynomial (P1) discontinuous Galerkin solution using a least-squares method. The stencils used in the reconstruction involve only the von Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG(P1P2) method is third-order accurate, and outperforms the third-order DG method (DG(P2)) in terms of both computing costs and storage requirements.

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