Vondraˇcek, Z.: An estimate for the L2-norm of a quasi continuous func- tion with respect to smooth measure, Arch. Math. 67 (1996), 408-414.Vondraček, Z.: ‘An estimate for the L 2 -norm of a quasi continuous function with respect to a smooth measure’, Arch. Math. 67 (...
Suppose that / 6 L\D) satisfies the wave equation A/ ■ \f, where A is the noneuclidean Laplacian, and further, assume that /is a common eigenfunction for all the Hecke operators. Then upper and lower bounds for the Z.2-norm of / are determined which depend only on A and the ...
For a function F(k):Z→Rm×n, the l∞ norm and l2 norm of F(k), if they exist, are respectively defined as ‖F(k)‖l∞≜supk∈Z{‖F(k)‖}, and ‖F(k)‖l2≜(∑k=0∞‖F(k)‖2)12. Finally, we define O(ε)≜{L(ε):(0,1]→R|limε→0+|L(ε)|=0} and...
{// ip = bf->l2Norm();}/// CREATE BCs ///Teuchos::RCP<BCEasy> bc = Teuchos::rcp(newBCEasy );// Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );SpatialFilterPtr left = Teuchos::rcp(newConstantXBoundary(-0.5) ); SpatialFilterPtr right = Teuchos::rcp(...
a function that assigns a strictly positive length or size to each vector in a vector space, except for the zero vector. ——Wikipedia 简单点说,一个向量的 norm 就是将该向量投影到 [0, ) 范围内的值,其中 0 值只有零向量的 norm 取到。看到这样的一个范围,相信大家就能想到其与现实中距离的类...
a function that assigns a strictly positive length or size to each vector in a vector space, except for the zero vector. ——Wikipedia 简单点说,一个向量的 norm 就是将该向量投影到 [0, ) 范围内的值,其中 0 值只有零向量的 norm 取到。看到这样的一个范围,相信大家就能想到其与现实中距离...
L1 norm就是绝对值相加,又称曼哈顿距离 L2 norm就是平方和开根号,又称欧几里德距离 在详细介绍L1与L2之前,先讲讲正则化的应用场景。 正则化方法:防止过拟合,提高泛化能力 所谓过拟合(over-fitting)其实就是所建的机器学习模型或者是深度学习模型在训练样本中表现得过于优越,导致在验证数据集以及测试数据集中表现不...
如何作为Loss Function 讲完了作为正则化项的内容了,那么讲讲L1、L2范数作为损失函数的情况。假设我们有一个线性回归模型,我们需要评估模型的效果,很常规的,我们会用“距离”来衡量误差! 若使用L1-norm来衡量距离,那就是我们的LAD(Least Absolute Deviation,最小绝对偏差),其优化的目标函数如下: ...
Modulation norms provide measures of joint time-frequency localization of a function f by replacing the L2-norm of the short-time Fourier transform of f by a mixed LP-norm. To have a firm understanding of how these norms measure smoothne... JA Hogan,JD Lakey 被引量: 108发表: 2001年 An...
如何作为Loss Function 讲完了作为正则化项的内容了,那么讲讲L1、L2范数作为损失函数的情况。假设我们有一个线性回归模型,我们需要评估模型的效果,很常规的,我们会用“距离”来衡量误差! 若使用L1-norm来衡量距离,那就是我们的LAD(Least Absolute Deviation,最小绝对偏差),其优化的目标函数如下: ...