We present a fast algorithm based on polynomial interpolation to approximate matrices arising from the discretization of second-kind integral equations where the kernel function is either smooth, non-oscillatory and p...We present a fast algorithm based on polynomial interpolation to approximate matrices arising from the discretization of second-kind integral equations where the kernel function is either smooth, non-oscillatory and possessing only a finite number of singularities or a product of such function with a highly oscillatory coefficient function. Contrast to wavelet-like approximations, ourapproximation matrix is not sparse. However, the approximation can be construced in O(n) operations and requires O(n) storage, where n is the number of quadrature points used in the discretization. Moreover, the matrix-vector multiplication cost is of order O(nlogn). Thus our scheme is well suitable for conjugate gradient type methods. Our numerical results indicate that the algorithm is very accurate and stable for high degree polynomial interpolation.展开更多
第三方资助(Third Party Funding,TPF)作为一种新兴的仲裁法律服务及投资模式,近年来受到理论界和实务界日益广泛的关注。第三方资助因其有利于国际商事仲裁的当事人减少高昂的仲裁成本,促进其维护自身的合法权益,而具有一定的现实必要...第三方资助(Third Party Funding,TPF)作为一种新兴的仲裁法律服务及投资模式,近年来受到理论界和实务界日益广泛的关注。第三方资助因其有利于国际商事仲裁的当事人减少高昂的仲裁成本,促进其维护自身的合法权益,而具有一定的现实必要性。然而,不可否认,第三方资助也给现行的仲裁制度带来了一系列法律挑战,包括"利益冲突""第三方对仲裁程序的控制"等。因此,国际社会普遍认为应当对这一行为进行适度的规制与监管。在本文中,笔者以比较法学的研究方法,比较了新加坡以及我国香港特别行政区对第三方资助的规制,尝试对我国内地未来第三方资助的规制方法提出建议。笔者认为,构建全面的信息披露制度是化解第三方资助行为法律挑战,促进第三方资助行为更好地实现其"接近正义"这一价值追求的核心与关键。展开更多
基金Research supported in part by Hong Kong Research Grant Council grats no.CUHK178/83E
文摘We present a fast algorithm based on polynomial interpolation to approximate matrices arising from the discretization of second-kind integral equations where the kernel function is either smooth, non-oscillatory and possessing only a finite number of singularities or a product of such function with a highly oscillatory coefficient function. Contrast to wavelet-like approximations, ourapproximation matrix is not sparse. However, the approximation can be construced in O(n) operations and requires O(n) storage, where n is the number of quadrature points used in the discretization. Moreover, the matrix-vector multiplication cost is of order O(nlogn). Thus our scheme is well suitable for conjugate gradient type methods. Our numerical results indicate that the algorithm is very accurate and stable for high degree polynomial interpolation.
文摘第三方资助(Third Party Funding,TPF)作为一种新兴的仲裁法律服务及投资模式,近年来受到理论界和实务界日益广泛的关注。第三方资助因其有利于国际商事仲裁的当事人减少高昂的仲裁成本,促进其维护自身的合法权益,而具有一定的现实必要性。然而,不可否认,第三方资助也给现行的仲裁制度带来了一系列法律挑战,包括"利益冲突""第三方对仲裁程序的控制"等。因此,国际社会普遍认为应当对这一行为进行适度的规制与监管。在本文中,笔者以比较法学的研究方法,比较了新加坡以及我国香港特别行政区对第三方资助的规制,尝试对我国内地未来第三方资助的规制方法提出建议。笔者认为,构建全面的信息披露制度是化解第三方资助行为法律挑战,促进第三方资助行为更好地实现其"接近正义"这一价值追求的核心与关键。