Random Iteration of Unimodal Linear Transformations

A Correction to "on the Iteration of Linear Homogeneous Transformations"

In the third paragraph of my paper Generalizations of the Bernoulli polynomials and numbers and corresponding summation formulas, published in this Bulletin, vol. 48 (1942), pp. 567-574, no explicit statement is made of the fact that it is assumed that P and Q as operators on x obey the laws: PF(x+c) ]c=0 = PF(x) ; QF(x+c)]c=0 = QF(x). Also the statement ƒ„(()) = 0, should read fn(0) = 0, n>0.

Analysis of transformations of linear random-effects models

Assume that a linear random-effects model (LRM) y = Xβ +ε = Xβ +ε with β = Aα+γ is transformed as Ty = TXβ + Tε = TXAα + TXγ + Tε by pre-multiplying a given matrix T. Estimations/predictions of the unknown parameters under the two models are not necessarily the same because the transformation matrix T occurs in the statistical inference of the transformed model. This paper presents a general al...

On One-Sided Ideals of Rings of Linear Transformations

Laws of Large Numbers for Random Linear

The computational solution of large scale linear programming problems contains various difficulties. One of the difficulties is to ensure numerical stability. There is another difficulty of a different nature, namely the original data, contains errors as well. In this paper, we show that the effect of the random errors in the original data has a diminishing tendency for the optimal value as the...

A Unifying Framework for Iteration Reordering Transformations

We present a framework for unifying iteration reordering transformations such as loop interchange, loop distribution, skewing, tiling, index set splitting and statement reordering. The framework is based on the idea that a transformation can be represented as a mapping from the original iteration space to a new iteration space. The framework is designed to provide a uniform way to represent and...