Related papers: Roundoff error analysis of the double exponential …
We introduce a new method for Estimation of Signal Parameters based on Iterative Rational Approximation (ESPIRA) for sparse exponential sums. Our algorithm uses the AAA algorithm for rational approximation of the discrete Fourier transform…
Several methods for computing the action of the matrix exponential $\mathrm{e}^{\boldsymbol{A}} \boldsymbol{b}$ are expressed by substituting $\boldsymbol{A}$ into a rational approximation of the scalar exponential function. The error of…
A formula is given for the propagation of errors during matrix inversion. An explicit calculation for a 2 by 2 matrix using both the formula and a Monte Carlo calculation are compared. A prescription is given to determine when a matrix with…
Leverage scores, loosely speaking, reflect the importance of the rows and columns of a matrix. Ideally, given the leverage scores of a rank-$r$ matrix $M\in\mathbb{R}^{n\times n}$, that matrix can be reliably completed from just…
A method is presented to tackle the sign problem in the simulations of systems having indefinite or complex-valued measures. In general, this new approach is shown to yield statistical errors smaller than the crude Monte Carlo using…
We give an efficient algorithm which can obtain a relative error approximation to the spectral norm of a matrix, combining the power iteration method with some techniques from matrix reconstruction which use random sampling.
This paper presents three quantitative sampling methods for reconstructing extended sources of the biharmonic wave equation using scattered field data. The first method employs an indicator function that solely relies on scattered fields $…
We present efficient approximation of the error function obtained by Fourier expansion of the exponential function $\exp [{- {(t - 2 \sigma)^2}/4}]$. The error analysis reveals that it is highly accurate and can generate numbers that match…
Code verification plays an important role in establishing the credibility of computational simulations by assessing the correctness of the implementation of the underlying numerical methods. In computational electromagnetics, the numerical…
Towards a solution to the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the…
Wu, Lou, Lai and Chang proposed a multi-exponentiation algorithm using binary complements and the non-adjacent form. The purpose of this paper is to show that neither the analysis of the algorithm given by its original proposers nor that by…
An algorithm for numerically computing the exponential of a matrix is presented. We have derived a polynomial expansion of $e^x$ by computing it as an initial value problem using a symbolic programming language. This algorithm is shown to…
Matrix completion is one of the key problems in signal processing and machine learning. In recent years, deep-learning-based models have achieved state-of-the-art results in matrix completion. Nevertheless, they suffer from two drawbacks:…
We construct fast, structure-preserving iterations for computing the sign decomposition of a unitary matrix $A$ with no eigenvalues equal to $\pm i$. This decomposition factorizes $A$ as the product of an involutory matrix $S =…
Two quadrature-based algorithms for computing the matrix fractional power $A^\alpha$ are presented in this paper. These algorithms are based on the double exponential (DE) formula, which is well-known for its effectiveness in computing…
This paper proposes a parametric error analysis method for Goldschmidt floating point division, which reveals how the errors of the intermediate results accumulate and propagate during the Goldschmidt iterations. The analysis is developed…
The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with $N$ samples behaves like $1/\sqrt{N}$. This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in…
We derive two probabilistic bounds for the relative forward error in the floating point summation of $n$ real numbers, by representing the roundoffs as independent, zero-mean, bounded random variables. The first probabilistic bound is based…
We propose a new instruction (FPADDRE) that computes the round-off error in floating-point addition. We explain how this instruction benefits high-precision arithmetic operations in applications where double precision is not sufficient.…
A generalized matrix-pencil approach is proposed for the estimation of complex exponential components with segmented signal samples, which is very efficient and provides super-resolution estimations. It is applicable to the signals sampled…