Related papers: On some randomized algorithms and their evaluation
Some randomized algorithms, used to obtain a random $n^2 \times n^2$ Sudoku matrix, where $n$ is a natural number, is reviewed in this study. Below is described the set $\Pi_n$ of all $(2n) \times n$ matrices, consisting of elements of the…
This work examines the problem to describe an efficient algorithm for obtaining $n^2 \times n^2$ Sudoku matrices. For this purpose, we define the concepts of $n\times n$ $\Pi_n$-matrix and disjoint $\Pi_n$-matrices. The article, using the…
Given some binary matrix $M$, suppose we are presented with the collection of its rows and columns in independent arbitrary orderings. From this information, are we able to recover the unique original orderings and matrix? We present an…
In this article we discuss the presentation of a random binary matrix using sequence of whole nonnegative numbers. We examine some advantages and disadvantages of this presentation as an alternative of the standard presentation using…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…
This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…
We provide several algorithms for the exact, uniform random sampling of Latin squares and Sudoku matrices via probabilistic divide-and-conquer (PDC). Our approach divides the sample space into smaller pieces, samples each separately, and…
We discuss the question of how to pick a matrix uniformly (in an appropriate sense) at random from groups big and small. We give algorithms in some cases, and indicate interesting problems in others.
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
In [Journal of Statistical Planning and Inference (141) (2011) 3697-3704], Roberto Fontana offers an algorithm for obtaining Sudoku matrices. Introduced by Geir Dahl concept disjoint pairs of S-permutation matrices [Linear Algebra and its…
In this note, following suggestions by Tao, we extend the randomized algorithm for linear equations over prime fields by Raghavendra to a randomized algorithm for linear equations over the reals. We also show that the algorithm can be…
The complexity of matrix multiplication is a central topic in computer science. While the focus has traditionally been on exact algorithms, a long line of literature also considers randomized algorithms, which return an approximate solution…
An algorithm for obtaining all n\times n binary matrices having exactly 2 units in every row and every column is described in the paper. After analysing the work of the algorithm a formula for calculating the number of these matrices has…
Some aspects of programming education are examined in this work. It is emphasised, based on the entertainment value, the most appropriate examples are chosen to demonstrate the different language constructions and data structures. Such an…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
An iterative randomness extraction algorithm which generalized the Von Neumann's extraction algorithm is detailed, analyzed and implemented in standard C++. Given a sequence of independently and identically distributed biased Bernoulli…
In this short paper we present an algorithm for finding a solution to a generalized Sudoku.
Recently much effort has been made towards the introduction of non-Hermitian random matrix models respecting $PT$-symmetry. Here we show that there is a one-to-one correspondence between complex $PT$-symmetric matrices and split-complex and…
The Randomized Kaczmarz Algorithm is a randomized method which aims at solving a consistent system of over determined linear equations. This note discusses how to find an optimized randomization scheme for this algorithm, which is related…