1994
DOI: 10.1515/rnam.1994.9.2.179
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The algorithm structure and V-matrices

Abstract: This is a brief survey devoted to K-matrices, which can be used not only for describing the structure of an algorithm but can also provide some additional information about it. We show the way K-matrices appear in such applications as the roundoff error analysis, the fast computation of gradients, and the complexity evaluation of linear algorithms. A perfectly simple procedure for deriving a fast algorithm for computing gradients is proposed. We also discuss some lower bounds for linear algorithms based on a d… Show more

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“…However, in many problems, in particular those discussed below, one needs to compute sums of the form Equation (10), in which the function A(l), −(N − 1) ≤ l ≤ (N − 1) is arbitrary in the specified range. Such sums arise when multiplying Toeplitz matrices by the vector [31,32]. This function A(l) is defined at the (2N − 1) integer point.…”
Section: Methodsmentioning
confidence: 99%
“…However, in many problems, in particular those discussed below, one needs to compute sums of the form Equation (10), in which the function A(l), −(N − 1) ≤ l ≤ (N − 1) is arbitrary in the specified range. Such sums arise when multiplying Toeplitz matrices by the vector [31,32]. This function A(l) is defined at the (2N − 1) integer point.…”
Section: Methodsmentioning
confidence: 99%