Related papers: An improved Talbot method for numerical Laplace tr…
A discrete Laplace transform and its inversion formula are obtained by using a quadrature of the continuous Fourier transform which is given in terms of Hermite polynomials and its zeros. This approach yields a convergent discrete formula…
In limited data computerized tomography, the 2D or 3D problem can be reduced to a family of 1D problems using the differentiated backprojection (DBP) method. Each 1D problem consists of recovering a compactly supported function $f \in…
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured…
We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in…
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
We analyze convergence of the Levenberg-Marquardt method for solving nonlinear inverse problems in Hilbert spaces. Specifically, we establish local convergence and convergence rates for a class of inverse problems that satisfy H\"{o}lder…
In many stochastic models, the observables of interest are naturally encoded in double transforms (e.g., Laplace transforms) that couple spatial and temporal variables. Notably, the double transform often provides the only analytically…
The inverse Laplace transform can turn a linear differential equation on a complex domain into an equivalent Volterra integral equation on a real domain. This can make things simpler: for example, a differential equation with irregular…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…
Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the…
This paper focuses on the mathematical approaches to the analysis of stability that is a crucial step in the design of dynamical systems. Three methods are presented, namely, absolutely integrable impulse response, Fourier integral, and…
This note briefly introduces the computed torque control method for trajectory tracking. The method is applicable to fully actuated robots, i.e, those whose inverse dynamics can be solved for any feasible acceleration. This includes many…
We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fast inverse square root algorithm and have the same or…
A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…
The Lorentz integral transform method is briefly reviewed. The issue of the inversion of the transform, and in particular its ill-posedness, is addressed. It is pointed out that the mathematical term ill-posed is misleading and merely due…
We introduce Tangent Attention Fine-Tuning (TAFT), a method for fine-tuning linearized transformers obtained by computing a First-order Taylor Expansion around a pre-trained initialization. We show that the Jacobian-Vector Product resulting…
In this paper, we present a novel method to compute an explicit formula for the inverse of the confluent Vandermonde matrices. Our proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences,…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…