English
Related papers

Related papers: Note: interpreting iterative methods convergence w…

200 papers

In this paper, we deal with distributed estimation problems in diffusion networks with heterogeneous nodes, i.e., nodes that either implement different adaptive rules or differ in some other aspect such as the filter structure or length, or…

Systems and Control · Computer Science 2017-09-05 Jesus Fernandez-Bes , Jerónimo Arenas-García , Magno T. M. Silva , Luis A. Azpicueta-Ruiz

We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…

Numerical Analysis · Mathematics 2020-03-31 S. Armstrong , A. Hannukainen , T. Kuusi , J. -C. Mourrat

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…

Machine Learning · Computer Science 2024-05-21 Hyungjin Chung , Byeongsu Sim , Dohoon Ryu , Jong Chul Ye

The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…

Numerical Analysis · Mathematics 2020-06-18 Leif Bergerhoff , Marcelo Cárdenas , Joachim Weickert , Martin Welk

For an equation of state in which pressure is a function only of density, the analysis of Newtonian stellar structure is simple in principle if the system is axisymmetric, or consists of a corotating binary. It is then required only to…

Solar and Stellar Astrophysics · Physics 2010-08-12 Richard H. Price , Charalampos Markakis , John L. Friedman

It is well known that a fixed point iteration for solving a linear equation system converges if and only if the spectral radius of the iteration matrix is less than one. A method is presented which guarantees the Fixed Point, even if this…

Numerical Analysis · Computer Science 2020-12-22 Hubert Karl , Sebstian Karl

The classical Ka\v{c}anov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates a given approximation by solving a linear problem in each step. Based on this observation,…

Numerical Analysis · Mathematics 2021-11-30 Pascal Heid , Thomas P. Wihler

We present a framework to use recently introduced Capsule Networks for solving the problem of Optical Flow, one of the fundamental computer vision tasks. Most of the existing state of the art deep architectures either uses a correlation…

Computer Vision and Pattern Recognition · Computer Science 2023-12-05 Rahul Chand , Rajat Arora , K Ram Prabhakar , R Venkatesh Babu

The description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach from the literature is shown to fail to produce the correct…

Computational Physics · Physics 2017-03-13 Clemens Mueller-Gugenberger , Robert Spatschek , Klaus Kassner

We introduce a novel, training-free method for sampling differentiable representations (diffreps) using pretrained diffusion models. Rather than merely mode-seeking, our method achieves sampling by "pulling back" the dynamics of the…

Computer Vision and Pattern Recognition · Computer Science 2024-12-11 Yash Savani , Marc Finzi , J. Zico Kolter

We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution…

Numerical Analysis · Mathematics 2020-01-27 Wesley Davis , Richard Noren , Ke Shi

Generalized diffusion type equations are considered and point symmetry analysis is applied to them. The equations with extremal order point symmetry algebras are described. Some old geometrical results are rederived in connection with…

Analysis of PDEs · Mathematics 2007-05-23 V. V. Dmitrieva , E. G. Neufeld , R. A. Sharipov , A. A. Tsaregorodtsev

We provide a careful Fourier analysis of the Guermond-Pasquetti mass lumping correction technique [Guermond J.-L., Pasquetti R. A correction technique for the dispersive effects of mass lumping for transport problems. - Computer Methods in…

Numerical Analysis · Mathematics 2018-11-12 Sergii Siryk

The Colebrook equation $\zeta$ is implicitly given in respect to the unknown flow friction factor $\lambda$; $\lambda=\zeta(Re,\epsilon^*,\lambda)$ which cannot be expressed explicitly in exact way without simplifications and use of…

Numerical Analysis · Computer Science 2018-10-29 Pavel Praks , Dejan Brkic

We revisit the classical problem of liquid imbibition in a single pore with spatially varying wettability. Starting from the Lucas-Washburn equation, we derive analytical solutions for the imbibition time (crossing time) in systems where…

Fluid Dynamics · Physics 2026-01-13 Mathis Fricke , Lisanne Gossel , Joel De Coninck

In this paper, we present a local convergence analysis of the self-consistent field (SCF) iteration using the density matrix as the state of a fixed-point iteration. Sufficient and almost necessary conditions for local convergence are…

Numerical Analysis · Mathematics 2018-11-26 Parikshit Upadhyaya , Elias Jarlebring , Emanuel H. Rubensson

A three-point iterative method for solving scalar non-linear equations was selected and then adapted to solve systems of non-linear equations. Subsequently, by applying Taylor's theorem to functions of $\R^{n}$ in $\R^{n}$, it is shown that…

General Mathematics · Mathematics 2026-01-23 Carlos E. Cadenas R. , Yorman J. Mendoza N

In this paper, we present a second-order accurate finite-difference method for solving convectiondiffusion equations with interfacial jumps on a moving interface. The proposed method is constructed under a semi-Lagrangian framework for…

Numerical Analysis · Mathematics 2020-05-29 Hyuntae Cho , Yesom Park , Myungjoo Kang

Multiphase flows are characterized by sharp moving interfaces, separating different fluids or phases. In many cases the dynamics of the interface determines the behavior of the flow. In a coarse, or reduced order model, it may therefore be…

Fluid Dynamics · Physics 2021-08-12 Xianyang Chen , Jiacai Lu , Gretar Tryggvason

A new iterative projection method is proposed to solve the unsteady Navier-Stokes equations with high Reynolds numbers. The convectional projection method attempts to project the intermediate velocity to the divergence free space only once…

Numerical Analysis · Mathematics 2025-10-02 Xiaoming Zheng , Kun Zhao , Jiahong Wu , Weiwei Hu , Dapeng Du