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 کاملToeplitz transforms of Fibonacci sequences
We introduce a matricial Toeplitz transform and prove that the Toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. We investigate the injectivity of this transform and show how this distinguishes the Fibonacci sequence among other recurrence sequences. We then obtain new Fibonacci identities as an application of our transform.
متن کاملFast superoptimal preconditioning of multiindex Toeplitz matrices
In this article three well-known methods of circulant preconditioning of finite multiindex Toeplitz linear systems, that is linear systems indexed by integers i1, . . ., id with 0 is < ns (s = 1, . . ., d), are studied in detail. A general algorithm for the construction of the so-called superoptimal preconditioner is also given and it is shown that this procedure requires O(n1 · · · nd log(n1 ·...
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...
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The Johnson-Lindenstrauss lemma is one of the corner stone results in dimensionality reduction. It says that given N , for any set of N vectors X ⊂ Rn, there exists a mapping f : X → Rm such that f(X) preserves all pairwise distances between vectors in X to within (1 ± ε) if m = O(ε lgN). Much effort has gone into developing fast embedding algorithms, with the Fast JohnsonLindenstrauss transfor...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1995
ISSN: 0024-3795
DOI: 10.1016/0024-3795(94)00043-3