Jorma K. Merikoski

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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 explanation of this phenomena when the image reconstruction problem of interest has least squares form. The benefits of using this natural constraint suggest the(More)
We present an asymptotic formula for the number of line segments connecting q + 1 points of an n × n square grid, and a sharper formula, assuming the Riemann hypothesis. We also present asymptotic formulas for the number of lines through at least q points and, respectively, through exactly q points of the grid. The well-known case q = 2 is so generalized.
where suB denotes the sum of the entries of a matrix B and m ≥ 0 (define 0 = 1). Hoffman’s proof was based on certain properties of stochastic matrices. Much later, in 1985, Sidorenko [9], without knowing Hoffman’s work, gave an independent proof as an elementary application of Hölder’s inequality. In 1990, Virtanen [10] generalized (1.1) to the(More)
The rank subtractivity partial ordering is defined on Cn×n (n ≥ 2) by A ≤− B⇔ rank(B−A) = rankB− rankA, and the star partial ordering by A ≤∗ B⇔ A∗A = A∗B ∧ AA∗ = BA∗. If A and B are normal, we characterize A ≤− B. We also show that then A ≤− B ∧ AB = BA⇔ A ≤∗ B⇔ A ≤− B ∧ A ≤− B. Finally, we remark that some of our results follow from well-known results on(More)
Abstract. Consider a finite, simple, undirected, and bipartite graph G with vertex sets V = {v1, . . . , vm} and W = {w1, . . . , wn}, m ≤ n, V ∩ W = ∅. Let the vertices of V have degrees d1 ≥ d2 ≥ · · · ≥ dm > 0, respectively. Let Ni be the set of neighbors of vi (i = 1, . . . ,m). Define dij = |Ni ∩Nj | (i, j = 1, . . . ,m), where | . | stands for the(More)