We propose new techniques and algorithms for the solution of a poly nomial system of equations by matrix methods For such a system we seek its speci ed root at which a xed polynomial takes its maximum or minimum absolute value on the set of roots We unify several known ap proaches and simplify the solution substantially in particular in the case of an overconstrained polynomial system having on...

Let A be a square matrix of order n with complex numbers as elements. The equation |XJ—A | = 0 is called the characteristic equation of the matrix A, and the roots X;, the characteristic roots of the matrix A. Although it is not possible to make any definite statements regarding the nature of the characteristic roots for the general matrix, several authors have given upper limits to the roots. ...

In this paper, an improvement to the mid-point method is contributed for finding square root of a matrix as well its inverse. To aim, iteration scheme find function constructed, and error stability estimates are provided show theoretical rate convergence. Our higher-order can compete with existing iterative methods similar nature. This illustrated in numerical simulations various sizes.

a consortium of biofertilizers (azotobacter chroococcum and bacillus subtilis) was applied in conventional as well as organic matrix entrapped granular forms as sole nutrient source in two different doses for cultivation of wheat (triticum aestivum l. cv. pbw-343). a double dose of conventional biofertilizers increased the growth of wheat plants as measured on 30, 60, 90, and 120 days after sow...

Univariate polynomial root-finding is both classical and important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the polynomial has no nonreal roots, but typically nonreal roots are much more numerous than the real ones. We dramatically accelerate the known algorithms in this case by...

The Q matrix invented by Baxter in 1972 to solve the eight vertex model at roots of unity exists for all values of N , the number of sites in the chain, but only for a subset of roots of unity. We show in this paper that a new Q matrix, which has recently been introduced and is non zero only for N even, exists for all roots of unity. In addition we consider the relations between all of the know...

In this paper we consider random block matrices which generalize the classical Laguerre ensemble and the Jacobi ensemble. We show that the random eigenvalues of the matrices can be uniformly approximated by the roots of matrix orthogonal polynomials and obtain a rate for the maximum difference between the eigenvalues and the roots. This relation between the random block matrices and matrix orth...

Abstract. A special class of recurrent neural network, termed Zhang neural network (ZNN) depicted in the implicit dynamics, has recently been proposed for online solution of time-varying matrix square roots. Such a ZNN model can be constructed by using monotonically-increasing odd activation functions to obtain the theoretical time-varying matrix square roots in an error-free manner. Different ...