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[en] The linear optimization algorithm ART3+O introduced by Chen et al (2010 Med. Phys. 37 4938–45) can efficiently solve large scale inverse planning problems encountered in radiation therapy by iterative projection. Its major weakness is that it cannot guarantee -optimality of the final solution due to an arbitrary stopping criterion. We propose an improvement to ART3+O where the stopping criterion is based on Farkas’ lemma. The same theory can be used to detect inconsistency in other projection methods as well. The proposed algorithm guarantees to find an -optimal solution in finite time. The algorithm is demonstrated on numerical examples in radiation therapy. (paper)
[en] Nekrasov matrices and nonsingular H-matrices are closely related. In this paper, Nekrasov tensors and S-Nekrasov tensors are proved to be nonsingular -tensors. And tensors are generalized Nekrasov tensors if and only if they are nonsingular -tensors. Furthermore, an iterative criterion for identifying nonsingular -tensors is provided.
[en] The characteristic interval plays a vital role on the existence of iterative roots of PM functions with height less than or equal to one. In this paper, we define the characteristic interval for continuous functions and prove theorems on extension and nonexistence of iterative roots for a class of continuous non-PM functions on a closed and bounded interval I. Also, we prove that a class of continuous non-PM functions, which do not possess any iterative roots, is dense in C(I, I).
[en] When functionally graded material layers are inserted between two impedance mismatching media, passbands with extremely large bandwidths can appear in these layered systems. An accurate and effective iterative method is developed to deal with these layered systems with extremely large layer number.
[en] In this paper we investigate normalization of rational functions, reducing in the sense of conjugation to monomials or more general power functions. We give conditions for the normalization by computing minimal irreducible decomposition of algebraic varieties. We use those conditions to compute the general n-th order iterates and iterative roots for those rational functions.
[en] The Sparse Matrix-Vector Multiplication (SpMV) is fundamental to a broad spectrum of scientific and engineering applications, such as many iterative numerical methods. The widely used Compressed Sparse Row (CSR) sparse matrix storage format was chosen to carry on this study for sustainability and reusability reasons. We parallelized for Intel Many Integrated Core (MIC) architecture a vectorized SpMV kernel using MPI and OpenMP, both pure and hybrid versions of them. In comparison to pure models and vendor-supplied BLAS libraries across different mainstream architectures (CPU, GPU), the hybrid model exhibits a substantial improvement. To further assess the behavior of hybrid model, we attribute the inadequacy of performances to vectorization rate, irregularity of non-zeros, and load balancing issue. A mathematical relationship between the first two factors and the performance is then proposed based on the experimental data. (authors)
[en] A linear resolution function in a physical measurement leads to data values and standard deviations at, say, N points. It is noted that the associated resolution functions may require that a number n of particular linear combinations of the data values be each not significantly different from zero. One is left with at most N-n parameters to evaluate. If the resolution functions are reasonably behaved, one can show that one sensible way to describe the underlying spectrum treats it as a linear combination of the given resolution functions and includes all the significant information from the data. An iterative search for the best component available to minimize the chi-square of the next fit to the data leads to a conjugate gradient technique. Programs based on the technique have been successfully used to obtain neutron spectra as a function of energy; in raw data from a pulse height analysis of proton recoils in a proportional counter, and where the raw data are time of flight spectra from a time dependent pulse of known form. It is planned to incorporate these, together with working programs respectively for photonuclear analysis and to explore the impurity concentration profile in a surface, into a single ''work-bench'' type program. A suitably difficult model unfolding problem has been developed and used to show the strengths and weaknesses of a number of other methods that have been used for unfolding