• Geophysics and Geophysical Exploration
• /
• v.7 no.3
• /
• pp.191-196
• /
• 2004

Seismic waveform inversion can be solved by using the classical Gauss-Newton method, which needs to construct the huge Hessian by the directly computed Jacobian. The property of Hessian mainly depends upon a source and receiver aperture, a velocity model, an illumination Bone and a frequency content of source wavelet. In this paper, we try to invert the Marmousi seismic data by controlling the huge Hessian appearing in the Gauss-Newton method. Wemake the two kinds of he approximate Hessian. One is the banded Hessian and the other is the approximate Hessian with automatic gain function. One is that the 1st updated velocity model from the banded Hessian is nearly the same of the result from the full approximate Hessian. The other is that the stability using the automatic gain function is more improved than that without automatic gain control.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.1
• /
• pp.1-10
• /
• 2010

In this note, we investigate the infinitesimal generators of the transformation groups induced by the Fourier-Gauss and Fourier-Mehler transforms on white noise functionals.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.3
• /
• pp.567-576
• /
• 2009

We classify and characterize the rational helicoidal surfaces in a three-dimensional Minkowski space satisfying pointwise 1-type like problem on the Gauss map.

• Communications of the Korean Mathematical Society
• /
• v.14 no.1
• /
• pp.189-200
• /
• 1999

In this paper, we proved that the only surfaces of 1-type Gauss map with flat normal connection are spheres, products of two plane circles and helical cylinders.

• Communications of the Korean Mathematical Society
• /
• v.27 no.1
• /
• pp.207-215
• /
• 2012

In this paper, we provide comparison results of several types of the preconditioned Gauss-Seidel methods for solving a linear system whose coefficient matrix is a Z-matrix. Lastly, numerical results are presented to illustrate the theoretical results.

• The Proceeding of the Korean Institute of Electromagnetic Engineering and Science
• /
• v.6 no.4
• /
• pp.20-27
• /
• 1995

A numerical simulation is carried out on the directivity synthesis of ultrasonic transducers by point source array. Gauss elimination method is practiced by means of a directive method to realize the desired directivity. Desired directivity is chosen to be that of a directivity of line source, a beam width and a direction arbitrary specified. On the numerical result, Gauss elimination method is showed high speed ca- lculative simulation and stability of system more than iterative method(LMS, DFP). Numerical simulations are carried out by PC(CPU:80486 DX2, RAM 16Mbyte).

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.2
• /
• pp.303-314
• /
• 2011

For Ax = b, it has recently been reported that the convergence of the preconditioned Gauss-Seidel iterative method which uses a matrix of the type P = I + S (${\alpha}$) to perform certain elementary row operations on is faster than the basic Gauss-Seidel method. In this paper, we discuss the adaptive Gauss-Seidel iterative method which uses P = I + S (${\alpha}$) + $\bar{K}({\beta})$ as a preconditioner. We present some comparison theorems, which show the rate of convergence of the new method is faster than the basic method and the method in [7] theoretically. Numerical examples show the effectiveness of our algorithm.

• Journal of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.381-397
• /
• 2017

In this paper, we study surfaces in 3-dimensional Minkowski space in terms of certain type of their Gauss map. We give several results on these surfaces whose Gauss map G satisfies ${\square}G=f(G+C)$ for a smooth function f and a constant vector C, where ${\square}$ denotes the ChengYau operator. In particular, we obtain classification theorems on the rotational surfaces in ${\mathbb{E}}^3_1$ with space-like axis of rotation in terms of type of their Gauss map concerning the Cheng-Yau operator.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.5
• /
• pp.1661-1668
• /
• 2015

We study the Gauss map G of ruled surfaces in the 3-dimensional Euclidean space $\mathbb{E}^3$ with respect to the so called Cheng-Yau operator ${\Box}$ acting on the functions defined on the surfaces. As a result, we establish the classification theorem that the only ruled surfaces with Gauss map G satisfying ${\Box}G=AG$ for some $3{\times}3$ matrix A are the flat ones. Furthermore, we show that the only ruled surfaces with Gauss map G satisfying ${\Box}G=AG$ for some nonzero $3{\times}3$ matrix A are the cylindrical surfaces.

• Journal of the Korean Mathematical Society
• /
• v.45 no.6
• /
• pp.1785-1801
• /
• 2008

Noncommutative extensions of the Gross and Beltrami Laplacians, called the quantum Gross Laplacian and the quantum Beltrami Laplacian, resp., are introduced and their basic properties are studied. As noncommutative extensions of the Fourier-Gauss and Fourier-Mehler transforms, we introduce the quantum Fourier-Gauss and quantum Fourier- Mehler transforms. The infinitesimal generators of all differentiable one parameter groups induced by the quantum Fourier-Gauss transform are linear combinations of the quantum Gross Laplacian and quantum Beltrami Laplacian. A characterization of the quantum Fourier-Mehler transform is studied.