[КНИГА][B] Inverse engineering handbook

KA Woodbury - 2002 - taylorfrancis.com
Inverse problems have been the focus of a growing number of research efforts over the last
40 years-and rightly so. The ability to determine a" cause" from an observed" effect" is a …

Fourier regularization for a backward heat equation

CL Fu, XT **ong, Z Qian - Journal of Mathematical Analysis and …, 2007 - Elsevier
In this paper a simple and convenient new regularization method for solving backward heat
equation—Fourier regularization method is given. Meanwhile, some quite sharp error …

A survey of regularization methods for first-kind Volterra equations

PK Lamm - Surveys on solution methods for inverse problems, 2000 - Springer
We survey continuous and discrete regularization methods for first-kind Volterra problems
with continuous kernels. Classical regularization methods tend to destroy the non …

[HTML][HTML] Tikhonov regularization method for a backward problem for the time-fractional diffusion equation

JG Wang, T Wei, YB Zhou - Applied Mathematical Modelling, 2013 - Elsevier
This paper is devoted to solve a backward problem for a time-fractional diffusion equation
with variable coefficients in a general bounded domain by the Tikhonov regularization …

Schr\" odingerisation based computationally stable algorithms for ill-posed problems in partial differential equations

S **, N Liu, C Ma - arxiv preprint arxiv:2403.19123, 2024 - arxiv.org
We introduce a simple and stable computational method for ill-posed partial differential
equation (PDE) problems. The method is based on Schr\" odingerization, introduced in [S …

Optimal stable approximations for the sideways heat equation

U Tautenhahn - 1997 - degruyter.com
In this paper we consider the following ill-posed Cauchy problem for the heat equation in the
half-plane: given noisy data us (L, i) to u (x, i) along the line χ= L, determine the solution u (x …

On the power of adaption

E Novak - Journal of Complexity, 1996 - Elsevier
Optimal error bounds for adaptive and nonadaptive numerical methods are compared. Since
the class of adaptive methods is much larger, a well-chosen adaptive method might seem to …

Two regularization methods for a Cauchy problem for the Laplace equation

Z Qian, CL Fu, ZP Li - Journal of Mathematical Analysis and Applications, 2008 - Elsevier
A Cauchy problem for the Laplace equation in a rectangle is considered. Cauchy data are
given for y= 0, and boundary data are for x= 0 and x= π. The solution for 0< y⩽ 1 is sought …

On a backward heat problem with time-dependent coefficient: Regularization and error estimates

TN Huy, QP Hoang, TD Duc, T Le Minh - Applied Mathematics and …, 2013 - Elsevier
In this paper, we consider a homogeneous backward heat conduction problem which
appears in some applied subjects. This problem is ill-posed in the sense that the solution (if …

Mollification and marching

DA Murio - Inverse engineering handbook, 2002 - books.google.com
The mollification method is a regularization procedure that is appropriate to stabilize a
variety of ill-posed problems by restoring continuity with respect to the data. The method can …