We present a number of results for elementary operations concerning the areas of data structures, computational geometry, graph algorithms and string algorithms. Especially, we focus on elementary operations like the dictionary operations, list manipulation, priority queues, temporal precedence, finger search, nearest common ancestors, negative cycle, 3-sided queries, rectangle enclosure, domin...

This paper proposes a reduct construction method based on discernibility matrix simplification. The method works in a similar way to the classical Gaussian elimination method for solving a system of linear equations. Elementary matrix simplification operations are introduced. Each operation transforms a matrix into a simpler form. By applying these operations a finite number of times, one can t...

This paper characterizes a class of regular para-Hermitian transfer matrices and then reveals the elementary characteristics of J -spectral factorization for this class. A transfer matrix in this class admits a J -spectral factorization if and only if there exists a common nonsingular matrix to similarly transform the A-matrices of and −1, resp., into 2 × 2 lower (upper, resp.) triangular block...

Two parallel block tridiagonalization algorithms and implementations for dense real symmetric matrices are presented. Block tridiagonalization is a critical pre-processing step for the block-tridiagonal divide-and-conquer algorithm for computing eigensystems and is useful for many algorithms desiring the efficiencies of block structure in matrices. For an “effectively” sparse matrix, which freq...

In this paper, we develop three essential ingredients of an algebraic structure theory of nite block Hankel matrices. The development centers around a transformation of block Hankel matrices, rst introduced by Fischer and Frobenius for scalar Hankel matrices. We prove three results: First, Iohvidov's fundamental notion of the characteristic of a Hankel matrix is extended to the block matrix cas...

We propose several variants of a secure multiparty computation protocol for AES encryption. The best variant requires 2200 + 400 255 expected elementary operations in expected 70 + 20 255 rounds to encrypt one 128-bit block with a 128-bit key. We implemented the variants using VIFF, a software framework for implementing secure multiparty computation (MPC). Tests with three players (passive secu...

This paper presents a new dual formulation for quadratically constrained convex programs (QCCP). The special structure of the derived dual problem allows to apply the gradient projection algorithm to produce a simple explicit method involving only elementary vector-matrix operations, that is proven to converge at a linear rate.

This paper gives a look-ahead Schur algorithm for nding the symmetric factorization of a Hermitian block Toeplitz matrix. The method is based on matrix operations and does not require any relations with orthogonal polynomials. The simplicity of the matrix based approach ought to shed new light on other issues such as parallelism and numerical stability.