Related papers: The Iris function and the matrix permanent
In this article, numerical integration is formulated as evaluation of a matrix function of a matrix that is obtained as a projection of the multiplication operator on a finite-dimensional basis. The idea is to approximate the continuous…
The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…
The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation [Moler C and van Loan C 1978 SIAM Review 20 4], none of which…
A polynomial-time algorithm for computing the permanent in any field of characteristic 3 is presented in this article. The principal objects utilized for that purpose are the Cauchy and Vandermonde matrices, the discriminant function and…
We introduce the concept of stable index for 0-1 matrices. Let $A$ be a 0-1 square matrix. If $A^k$ is a 0-1 matrix for every positive integer $k$, then the stable index of $A$ is defined to be infinity; otherwise, the stable index of $A$…
In this paper we give the absolutely new proof of a conjecture of R.F.Scott(1881) on the permanent of a Cauchy matrix $\ls \frac{1}{x_i-y_j} \rs_{1 \leqslant i,j \leqslant n},$ where $x_1, ..., x_n$ and $y_1, ..., y_n$ are the distinct…
We establish the first globally convergent algorithms for computing the Kreiss constant of a matrix to arbitrary accuracy. We propose three different iterations for continuous-time Kreiss constants and analogues for discrete-time Kreiss…
Let A be an n by n doubly substochastic matrix and denote {\sigma}(A) the sum of all elements of A. In this paper we give the upper bound of the permanent of (I-A) with respect to n and {\sigma}(A).
Let $M_{n}$ denote a random symmetric $n\times n$ matrix, whose entries on and above the diagonal are i.i.d. Rademacher random variables (taking values $\pm 1$ with probability $1/2$ each). Resolving a conjecture of Vu, we prove that the…
We establish a superpolynomial lower bound on the range of the permanent function on the set of $n\times n$ matrices with $\pm1$ entries.
Matrix permanents arise naturally in the context of linear optical networks fed with nonclassical states of light. In this letter we tie the computational complexity of a class of multi-dimensional integrals to the permanents of large…
For enumerative problems, i.e. computable functions f from N to Z, we define the notion of an effective (or closed) formula. It is an algorithm computing f(n) in the number of steps that is polynomial in the combined size of the input n and…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
In this paper we provide an identity between determinant and generalized matrix function. Also, a criterion of positive semi-definite matrices affirming the permanent dominant conjecture is given. As a consequence, infinitely many infinite…
For fixed natural numbers $r$ and $s$, where $2\leq s \leq r$, we consider a representation of numbers from the interval $[0;\frac{r}{s-1}]$ obtained by encoding numbers by means of the alphabet $A=\{0,1,...,r\}$ via the expansion…
The matrix permanent belongs to the complexity class #P-Complete. It is generally believed to be computationally infeasible for large problem sizes, and significant research has been done on approximation algorithms for the matrix…
Highly oscillatory integrals, such as those involving Bessel functions, are best evaluated analytically as much as possible, as numerical errors can be difficult to control. We investigate indefinite integrals involving monomials in $x$…
We obtain an iterative formula that converges incrementally to the smallest singular value. Similarly, we obtain an iterative formula that converges decreasingly to the largest singular value.
As well known, permanent of a square (0,1)-matrix $A$ of order $n$ enumerates the permutations $\beta$ of $1,2,...,n$ with the incidence matrices $B\leq A.$ To obtain enumerative information on even and odd permutations with condition…
We introduce the notion of matrices graph, defining continued fraction algorithms where the past and the future are almost independent. We provide an algorithm to convert more general algorithms into matrices graphs. We present an algorithm…