Related papers: On the Exponentiation of Interval Matrices
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
This paper presents the first study of the complexity of the optimization problem for integer linear-exponential programs which extend classical integer linear programs with the exponential function $x \mapsto 2^x$ and the remainder…
An algorithm for numerically computing the exponential of a matrix is presented. We have derived a polynomial expansion of $e^x$ by computing it as an initial value problem using a symbolic programming language. This algorithm is shown to…
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…
In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
The work is devoted to the development of numerical methods for computing "formal solutions" of interval systems of linear algebraic equations. These solutions are found in Kaucher interval arithmetic, which extends and completes the…
Many problems in optimization theory are strongly nonlinear in the traditional sense but possess a hidden linear structure over suitable idempotent semirings. After an overview of `Idempotent Mathematics' with an emphasis on matrix theory,…
Several methods for computing the action of the matrix exponential $\mathrm{e}^{\boldsymbol{A}} \boldsymbol{b}$ are expressed by substituting $\boldsymbol{A}$ into a rational approximation of the scalar exponential function. The error of…
The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…
In this paper, a rigorous computational method to enclose eigendecompositions of complex interval matrices is proposed. Each eigenpair $x=(\lambda,v)$ is found by solving a nonlinear equation of the form $f(x)=0$ via a contraction argument.…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…
Query evaluation in tuple-independent probabilistic databases is the problem of computing the probability of an answer to a query given independent probabilities of the individual tuples in a database instance. There are two main approaches…
We show an explicit formula, with a quite easy deduction, for the exponential matrix $e^{tA}$ of a real square matrix $A$ of order $n\times n$. The elementary method developed requires neither Jordan canonical form, nor eigenvectors, nor…
In this work, we consider a rational approximation of the exponential function to design an algorithm for computing matrix exponential in the Hermitian case. Using partial fraction decomposition, we obtain a parallelizable method, where the…
Many problems in computer science and applied mathematics require rounding a vector $\mathbf{w}$ of fractional values lying in the interval $[0,1]$ to a binary vector $\mathbf{x}$ so that, for a given matrix $\mathbf{A}$,…
The matrix exponential is a fundamental operator in scientific computing and system simulation, with applications ranging from control theory and quantum mechanics to modern generative machine learning. While Pad\'e approximants combined…
Inference algorithms based on evolving interactions between replicated solutions are introduced and analyzed on a prototypical NP-hard problem - the capacity of the binary Ising perceptron. The efficiency of the algorithm is examined…
In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…
Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome and hard to compute, theoretical methods: (1) average Hamiltonian theory following…