Sentence examples for expansion of kernel from inspiring English sources

To derive the multipole expansion of kernel (G y,x):=frac {1}{ y-x ^{m}}), we need the following formulation.

Based on the multipole expansion of kernel, we demonstrate that the approximate operator used in the collocation equation converges to the initial operator.

Second, we discuss the asymptotic distribution of eigenvalues by obtaining the asymptotic expansion of the kernel of semigroup.

We interchange differentiation and the application of F, which can be justified by using the homogeneous expansion of the kernel.

Based on the multipole expansion of the kernel, the FMM can be used to accelerate the matrix-vector multiplication.

The expansion of the kernel began from the tip of the grain and the model could successfully capture this phenomenon.

Development of large pressures within a soft matrix results in large volumetric expansion of the kernel causing it to puff.

Proof of Theorem 1.2 As above, we use the series expansion of a kernel K ( x, y ), the operator [ b →, T ] f ( x ) is divided into [ b →, T ] f ( x ) = ∑ s, m b s m ( x ) [ b →, T s m ] f ( x ).

It is easy to verify (using the homogeneous expansion of the kernel function) that F ( f r ) = ∫ B n f r ( w ) F z [ 1 ( 1 − 〈 z, w 〉 ) n + 1 + s ( 1 − | φ z ( w ) | 2 ) β ω ( 1 − | w | ) ] d ν s ( w ).

We lay down a mathematical foundation well fitted to this approach, which relies on the spectral expansion of Mercer kernels.

Our Nyström method has made use of the cancellation of leading terms in the series expansion of integral kernels to handle hyper singularities in near terms.