-The present paper deals with a modification on the selection of linear systematic sample of odd size. Consequently the proposed method is called modified linear systematic sampling. The performances of the modified linear systematic sampling are assessed with that of simple random sampling and linear systematic sampling for certain hypothetical populations. As a result, it is observed that the...

-The present paper deals with a modification on the selection of linear systematic sample of odd size. Consequently the proposed method is called modified linear systematic sampling. The performances of the modified linear systematic sampling are assessed with that of simple random sampling and linear systematic sampling for certain hypothetical populations. As a result, it is observed that the...

This article gives a short tutorial on the MUSIC algorithm and the linear sampling method of [3], and explains how the latter is an extension of the former. 1 MUSIC MUSIC is an abbreviation for MUltiple SIgnal Classification [10]; we see below why the name is appropriate. 1.1 The basics of MUSIC MUSIC is essentially a method of characterizing the range of a self-adjoint operator. Suppose is a s...

In this talk, we will be mainly concerned with a novel multilevel linear sampling method (MLSM) for reconstructing the obstacle from its corresponding scattering amplitude. The new method is shown to possess asymptotically optimal computational complexity. For an n×n sampling mesh in R2 or an n×n×n sampling mesh in R3, the proposed algorithm requires to solve only O(nN−1) far-field equations fo...

Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of the inclusion of a function in the range of an operator. Numerical examples are given to illustrate theoretical conclusions. Alternative methods of identification of obstacles are mentioned: the Support Function Method (SFM) and the Modified Rayleigh Conjecture (MRC) method. 1...

A lecture note introducing the sampling theorem as an interpolation method is presented. The relationship between piecewise linear approximation and the sampling theorem is highlighted by the use of triangular pulses instead of sampling functions. Furthermore, a comparison of the linear interpolation with a series on a nonorthogonal basis composed of equally spaced triangular pulses is provided...

A novel multilevel algorithm is presented for implementing the widely used linear sampling method in inverse obstacle scattering problems. The new method is shown to possess asymptotically optimal computational complexity. For an n×n sampling mesh in R2 or an n×n×n sampling mesh in R3, the proposed algorithm requires one to solve only O(nN−1) far-field equations for a RN problem (N=2,3), and th...

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