Fast computation of Toeplitz forms and some multidimensional integrals
نویسنده
چکیده
A fast algorithm is proposed for computation of certain multilevel Toeplitz forms. It helps to implement some simple quadrature formulas in an efficient way, allowing for the use of more nodes. An application example is given with the volume integral equations in electromagnetics.
منابع مشابه
Mean value theorem for integrals and its application on numerically solving of Fredholm integral equation of second kind with Toeplitz plus Hankel Kernel
The subject of this paper is the solution of the Fredholm integral equation with Toeplitz, Hankel and the Toeplitz plus Hankel kernel. The mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the method.
متن کاملFast computation of the matrix exponential for a Toeplitz matrix
The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured n×n matrix it can be computed in O(n3) operations. An interesting problem arises if the input matrix is a Toeplitz matrix, for example as the result of discretizing integral equations with a time invariant kernel. In this case it is not obvious how to take advantage of t...
متن کاملFast Cauchy-like and Singular Toeplitz-like Matrix Computations
computes the solution ~ x = T ?1 ~ b to a nonsingular Toeplitz or Toeplitz-like linear system T~ x = ~ b, a short displacement generator for the inverse T ?1 of T, and det T. We extend this algorithm to the similar computations with nn Cauchy (generalized Hilbert) and Cauchy-like matrices. Recursive triangular factorization of such a matrix can be computed by our algorithm at the cost of execut...
متن کاملComposite quadrature formulae for the approximation of wavelet coefficients of piecewise smooth and singular functions
The computation of wavelet coefficients of a function typically requires the computation of a large number of integrals. These integrals represent the inner product of that function with a wavelet function on different scales, or with the corresponding scaling function on a fine scale. We develop quadrature rules for those integrals that converge fast for piecewise smooth and singular functions...
متن کاملAccurate computation of Galerkin double surface integrals in the 3-D boundary element method
Many boundary element integral equation kernels are based on the Green’s functions of the Laplace and Helmholtz equations in three dimensions. These include, for example, the Laplace, Helmholtz, elasticity, Stokes, and Maxwell’s equations. Integral equation formulations lead to more compact, but dense linear systems. These dense systems are often solved iteratively via Krylov subspace methods, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007