Fast polynomial transforms based on Toeplitz and Hankel matrices
نویسندگان
چکیده
منابع مشابه
Fast Polynomial Transforms Based on Toeplitz and Hankel Matrices
Many standard conversion matrices between coefficients in classical orthogonal polynomial expansions can be decomposed using diagonally-scaled Hadamard products involving Toeplitz and Hankel matrices. This allows us to derive O(N(logN)) algorithms, based on the fast Fourier transform, for converting coefficients of a degree N polynomial in one polynomial basis to coefficients in another. Numeri...
متن کاملFast Algorithms for Toeplitz and Hankel Matrices
The paper gives a self-contained survey of fast algorithms for solving linear systems of equations with Toeplitz or Hankel coefficient matrices. It is written in the style of a textbook. Algorithms of Levinson-type and of Schur-type are discussed. Their connections with triangular factorizations, Padè recursions and Lanczos methods are demonstrated. In the case in which the matrices possess add...
متن کاملIrreducible Toeplitz and Hankel matrices
An infinite matrix is called irreducible if its directed graph is strongly connected. It is proved that an infinite Toeplitz matrix is irreducible if and only if almost every finite leading submatrix is irreducible. An infinite Hankel matrix may be irreducible even if all its finite leading submatrices are reducible. Irreducibility results are also obtained in the finite cases.
متن کاملFast Hankel Transforms
JOHANSEN, H. K., and SORENSEN, K., 1979, Fast Hankel Transforms, Geophysical Prospecting 27, 876-901. Inspired by the linear filter method introduced by D. P. Ghosh in rg7o we have developed a general theory for numerical evaluation of integrals of the Hankel type: m g(r) = Sf(A)hJ,(Ar)dh; v > I. II Replacing the usual sine interpolating function by sinsh (x) = a . sin (xx)/sinh (UTW), where th...
متن کاملBalanced Random Toeplitz and Hankel Matrices
Except for the Toeplitz and Hankel matrices, the common patterned matrices for which the limiting spectral distribution (LSD) are known to exist share a common property–the number of times each random variable appears in the matrix is (more or less) the same across the variables. Thus it seems natural to ask what happens to the spectrum of the Toeplitz and Hankel matrices when each entry is sca...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2017
ISSN: 0025-5718,1088-6842
DOI: 10.1090/mcom/3277