Related papers: Explicit error bound for modified numerical iterat…
The Sinc convolution is an approximate formula for indefinite convolutions proposed by Stenger. The formula was derived based on the Sinc indefinite integration formula combined with the single-exponential transformation. Although its…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
Simulations of the dynamics generated by partial differential equations (PDEs) provide approximate, numerical solutions to initial value problems. Such simulations are ubiquitous in scientific computing, but the correctness of the results…
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…
In this article we present a modified S-iteration process that we combine with inertial extrapolation to find a common solution to the split monotone inclusion problem and the fixed point problem in real Hilbert space.Our goal is to…
In engineering, it is a common desire to couple existing simulation tools together into one big system by passing information from subsystems as parameters into the subsystems under influence. As executed at fixed time points, this data…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
We describe various issues caused by the lack of round-to-nearest mode in the \textit{gcc} compiler implementation of the fixed-point arithmetic data types and operations. We demonstrate that round-to-nearest is not performed in the…
Iterative Refinement (IR) is a classical computing technique for obtaining highly precise solutions to linear systems of equations, as well as linear optimization problems. In this paper, motivated by the limited precision of quantum…
Obtaining the inverse of a large symmetric positive definite matrix $\mathcal{A}\in\mathbb{R}^{p\times p}$ is a continual challenge across many mathematical disciplines. The computational complexity associated with direct methods can be…
Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…
In this paper, we improve the usual relative error bound for the computation of x^n through iterated multiplications by x in binary floating-point arithmetic. The obtained error bound is only slightly better than the usual one, but it is…
Noise in quantum hardware remains the biggest roadblock for the implementation of quantum computers. To fight the noise in the practical application of near-term quantum computers, instead of relying on quantum error correction which…
We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all…
Although there is growing interest in measuring integrated information in computational and cognitive systems, current methods for doing so in practice are computationally unfeasible. Existing and novel integration measures are investigated…
A new error bound for the linear complementarity problem is given when the involved matrix is a B-matrix. It is shown that this bound is sharper than some previous bounds [C.Q. Li, Y.T. Li. Note on error bounds for linear complementarity…
Quantum error mitigation is a promising route to achieving quantum utility, and potentially quantum advantage in the near-term. Many state-of-the-art error mitigation schemes use knowledge of the errors in the quantum processor, which opens…
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
A priori error bounds have been derived for different balancing-related model reduction methods. The most classical result is a bound for balanced truncation and singular perturbation approximation that is applicable for asymptotically…
The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function…