CAJ | 학술논문

致力于讨论第一类强奇异积分方程的快速Fourier配置法。首先介绍了配置法基本框架，其次，根据核函数b（x ，y）的性质提出了一种矩阵压缩策略，使得矩阵的计算量由原来的 O（n2）减到 O（nlog n），并且压缩后的逼近方程几乎保持原逼近方程的性质。基于快速Fourier变换给出一种求积公式，最后用数值例子检验算法的有效性。
치력우토론제일류강기이적분방정적쾌속Fourier배치법。수선개소료배치법기본광가，기차，근거핵함수b（x ，y）적성질제출료일충구진압축책략，사득구진적계산량유원래적 O（n2）감도 O（nlog n），병차압축후적핍근방정궤호보지원핍근방정적성질。기우쾌속Fourier변환급출일충구적공식，최후용수치례자검험산법적유효성。
In this paper ,we focus on developing fast Fourier‐Collocation methods for the first kind of singular integral equations .Firstly ,we introduce the trigonometric collocation method for sol‐ving the first kind of singular integTal equations by choosing suitable collocation functionals and trial function spaces S.econdly ,we propose a truncation strategy which reduces the tile number of nonzero entries of the matrix from O(n2 ) to O (nlog n) ,but our trigonometric collocation method still pre‐serves the convergence property of the trigonometric collocation method .At last ,we give the quadra‐ture formula by the fast Fourier transform and illustrate the theoretical estimates by some numerical examples .