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Publications Influence

On eigenvalues of meet and join matrices associated with incidence functions

- Pauliina Ilmonen, P. Haukkanen, J. Merikoski
- Mathematics
- 1 August 2008

Abstract Let ( P , ⪯ , ∧ ) be a locally finite meet semilattice. Let S = { x 1 , x 2 , … , x n } , x i ⪯ x j ⇒ i ⩽ j , be a finite subset of P and let f be a complex-valued function on P . Then the n… Expand

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Inequalities for spreads of matrix sums and products.

- J. Merikoski, R. Kumar
- Mathematics
- 2004

Let A and B be complex matrices of same dimension. Given their eigen- values and singular values, we survey and further develop simple inequalities for eigenvalues and singular values of A + B, AB ,a… Expand

59 4- PDF

A best upper bound for the 2-norm condition number of a matrix

- J. Merikoski, Uoti Urpala, A. Virtanen, T. Tam, F. Uhlig
- Mathematics
- 15 March 1997

Abstract Let A be an n × n nonsingular real or complex matrix. The best possible upper bound for the ratio of the largest and smallest singular values of A, using tr A∗A , det A, and n only, is… Expand

31 2

Bounds for Eigenvalues Using the Trace and Determinant

- J. Merikoski, A. Virtanen
- Mathematics
- 1 October 1997

Abstract Let A be a square matrix with real and positive eigenvalues λ 1 ⩾ … ⩾ λ n > 0, and let 1 ≤ k ≤ l ≤ n . Bounds for λ kl … λ l and λ k + … + λ l , involving k, l, n, tr A , and det A only, are… Expand

23 2- PDF

Mathematical Modelling

- Matti Heili, Timo Lhivaara, +11 authors M. Vauhkonen
- Computer Science
- 14 July 2016

TLDR

3 2

ON THE STAR PARTIAL ORDERING OF NORMAL MATRICES

- J. Merikoski, Xiaoji Liu
- Mathematics
- 2006

We order the space of complex n× n matrices by the star partial ordering ≤∗. So A ≤∗ B means that A∗A = A∗B andAA∗ = BA∗. We find several characterizations for A ≤∗ B in the case of normal matrices.… Expand

11 2- PDF

Characterizations and lower bounds for the spread of a normal matrix

- J. Merikoski, R. Kumar
- Mathematics
- 1 May 2003

Abstract The spread of an n×n matrix A with eigenvalues λ1,…,λn is defined by spr A = max j,k |λ j −λ k |. We prove that if A is normal, then spr A = max | x * Ax − y * Ay | | x , y ∈ C n ,∥ x ∥=∥ y… Expand

27 2- PDF

THE STABILIZING PROPERTIES OF NONNEGATIVITY CONSTRAINTS IN LEAST-SQUARES IMAGE RECONSTRUCTION

The incorporation of nonnegativity constraints in image reconstruction problems is known to have a stabilizing effect on solution methods. In this paper, we both demonstrate and provide an… Expand

20 1- PDF

Bounds for singular values using traces

- J. Merikoski, H. Sarria, P. Tarazaga
- Mathematics
- 1 October 1994

Abstract Bounds for the singular values, ratios of singular values, and rank of a square matrix A , involving tr A , tr A 2 , and tr A H A , are presented. Some of the results are analogous to the… Expand

21 1

A simple proof for the inequality between the perron root of a nonnegative matrix and that of its geometric symmetrization

- Yu. A. Al’pin, J. Merikoski
- Mathematics
- 8 September 2010

AbstractLet A = (aij) be a nonnegative square matrix, let G = (gij) be its geometric symmetrization, i.e., gij = $$
\sqrt {a_{ij} a_{ji} }
$$, and let ρ denote the Perron root. We present a simple… Expand

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