Related papers: Sample programs in C++ for matrix computations in …
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
We introduce the smt toolbox for Matlab. It implements optimized storage and fast arithmetics for circulant and Toeplitz matrices, and is intended to be transparent to the user and easily extensible. It also provides a set of test matrices,…
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic…
We introduce the C++ library Wedge, based on GiNaC, for symbolic computations in differential geometry. We show how Wedge makes it possible to use the language C++ to perform such computations, and illustrate some advantages of this…
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…
Quantum trajectory methods can be used for a wide range of open quantum systems to solve the master equation by unraveling the density operator evolution into individual stochastic trajectories in Hilbert space. This C++ class library…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
Tantrix is a puzzle to make a loop by connecting lines drawn on hexagonal tiles, and the objective of this research is to solve it by a computer. For this purpose, we give a problem setting of solving Tantrix as arranging tiles in an…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
Quantum++ is a modern general-purpose multi-threaded quantum computing library written in C++11 and composed solely of header files. The library is not restricted to qubit systems or specific quantum information processing tasks, being…
In this era of diverse and heterogeneous computer architectures, the programmability issues, such as productivity and portable efficiency, are crucial to software development and algorithm design. One way to approach the problem is to step…
We present a collection of modular open source C++ libraries for the development of logic synthesis applications. These libraries can be used to develop applications for the design of classical and emerging technologies, as well as for the…
Mathematical software has traditionally been built in the form of "packages" that build on each other. A substantial fraction of these packages is written in C++ and, as a consequence, the interface of a package is described in the form of…
We present ZERO, a modular and extensible C++ library interfacing Mathematical Programming and Game Theory. ZERO provides a comprehensive toolkit of modeling interfaces and algorithms for Reciprocally Bilinear Games (RBGs), i.e.,…
Reduze is a computer program for reducing Feynman Integrals to master integrals employing a Laporta algorithm. The program is written in C++ and uses classes provided by the GiNaC library to perform the simplifications of the algebraic…
Software package for Monte-Carlo simulation of e+e- exclusive annihilation channels written in the C++ language for Linux/Solaris platforms has been developed. It incorporates matrix elements for several mechanisms of multipion production…
We present SLinGen, a program generation system for linear algebra. The input to SLinGen is an application expressed mathematically in a linear-algebra-inspired language (LA) that we define. LA provides basic scalar/vector/matrix…
In this paper, several Kaczmarz-type numerical methods for solving the matrix equation $AX=B$ and $XA=C$ are proposed, where the coefficient matrix $A$ may be full rank or rank deficient. These methods are iterative methods without matrix…