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New bounds for the minimum eigenvalue of the Fan product of two M -matrices

Guanghui Cheng (2014)

Czechoslovak Mathematical Journal

In this paper, we mainly use the properties of the minimum eigenvalue of the Fan product of M -matrices and Cauchy-Schwarz inequality, and propose some new bounds for the minimum eigenvalue of the Fan product of two M -matrices. These results involve the maximum absolute value of off-diagonal entries of each row. Hence, the lower bounds for the minimum eigenvalue are easily calculated in the practical examples. In theory, a comparison is given in this paper. Finally, to illustrate our results, a simple...

New bounds for the minimum eigenvalue ofM-matrices

Feng Wang, Deshu Sun (2016)

Open Mathematics

Some new bounds for the minimum eigenvalue of M-matrices are obtained. These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices. Finally, some examples are also given to show that the bounds are better than some previous results.

New iterative codes for𝓗-tensors and an application

Feng Wang, Deshu Sun (2016)

Open Mathematics

New iterative codes for identifying 𝓗 -tensor are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor, i.e., an even-degree homogeneous polynomial form are given. Advantages of results obtained are illustrated by numerical examples.

New results about semi-positive matrices

Jonathan Dorsey, Tom Gannon, Charles R. Johnson, Morrison Turnansky (2016)

Czechoslovak Mathematical Journal

Our purpose is to present a number of new facts about the structure of semipositive matrices, involving patterns, spectra and Jordon form, sums and products, and matrix equivalence, etc. Techniques used to obtain the results may be of independent interest. Examples include: any matrix with at least two columns is a sum, and any matrix with at least two rows, a product, of semipositive matrices. Any spectrum of a real matrix with at least 2 elements is the spectrum of a square semipositive matrix,...

New stability conditions for positive continuous-discrete 2D linear systems

Tadeusz Kaczorek (2011)

International Journal of Applied Mathematics and Computer Science

New necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.

Nonsingularity, positive definiteness, and positive invertibility under fixed-point data rounding

Jiří Rohn (2007)

Applications of Mathematics

For a real square matrix A and an integer d ≥ 0 , let A ( d ) denote the matrix formed from A by rounding off all its coefficients to d decimal places. The main problem handled in this paper is the following: assuming that A ( d ) has some property, under what additional condition(s) can we be sure that the original matrix A possesses the same property? Three properties are investigated: nonsingularity, positive definiteness, and positive invertibility. In all three cases it is shown that there exists a real number...

Note on the core matrix partial ordering

Jacek Mielniczuk (2011)

Discussiones Mathematicae Probability and Statistics

Complementing the work of Baksalary and Trenkler [2], we announce some results characterizing the core matrix partial ordering.

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