This paper considers the problem of minimizing roundoff noise in two-dimensional (2-D) state-space digital filters subject to L2-norm dynamic-range scaling constraints. The minimization will be achieved by using error feedback. Several techniques for the determination of the optimal full-scale, block-diagonal, diagonal, and scalar error-feedback matrices for a given 2-D statespace digital filte...

We study permuting and batched orthogonal geometric reporting problems in the External Memory Model (EM), assuming indivisibility of the input records. Our main results are twofold. First, we prove a general simulation result that essentially shows that any permutation algorithm (resp. duplicate removal algorithm) that does αN/B I/Os (resp. to remove a fraction of the existing duplicates) can b...

In this paper we describe a dynamic external memory data structure that supports range reporting queries in three dimensions in O(logB N + k B ) I/O operations, where k is the number of points in the answer and B is the block size. This is the first dynamic data structure that answers three-dimensional range reporting queries in log O(1)

We study the one-dimensional range minimum query (RMQ) problem in the external memory model. We provide the first spaceoptimal solution to the batched static version of the problem. On an instance with N elements and Q queries, our solution takes Θ(sort(N + Q)) = Θ ( N+Q B logM/B N+Q B ) I/O complexity and O(N + Q) space, where M is the size of the main memory and B is the block size. This is a...

In this paper, we use a combination of Legendre and Block-Pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.The nonlinear part of the integral equation is approximated by Hybrid Legen-dre Block-Pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. We give some numerical examples. To showapplicability of...