Abstract Multi-spectral CT (MSCT) is increasingly used in industrial non-destructive testing and medical diagnosis because of its outstanding performance like material distinguishability. The process obtaining MSCT data can be modeled as a nonlinear system the basis decomposition comes down to inverse problem system. For different spectra data, geometric inconsistent parameters cause geometrica...

We introduce a novel approach for structure activity relationship analysis based on the use of a special kernel. The kernel eÆciently performs Gram-Schmidt orthogonalisation in a kernel de ned feature space. We show that support vector machines in conjunction with Gram-Schmidt kernel, a recent method to extract features, can be adopted successfully to predict the inhibition of dihydrofolate red...

Solving a set of linear equations arises in many contexts in applied mathematics. At least until recently, a claim could be made that solving sets of linear equations (generally as a component of dealing with larger problems like partial-differential-equation solving, or optimization, consumes more computer time than any other computational procedure. (Distant competitors would be the Gram-Schm...

In various situations requiring empirical model building from highly multivariate measurements, modelling based on partial least squares regression (PLSR) may often provide efficient low-dimensional solutions. unsupervised situations, the same be true for principal component analysis (PCA). both cases, however, it is also of interest to identify subsets measured variables useful obtaining spars...

Active metric learning is the problem of incrementally selecting high-utility batches training data (typically, ordered triplets) to annotate, in order progressively improve a learned model over some input domain as rapidly possible. Standard approaches, which independently assess informativeness each triplet batch, are susceptible highly correlated with many redundant triplets and hence low ov...

The Gram-Schmidt procedure is used to orthogonalize one vector against a set of vectors or to construct a QR factorization of a matrix. In the Classical Gram-Schmidt algorithm (CGS), orthogonal vectors are produced via matrix{vector updates, which is desirable for parallel computers. Unfortunately, this algorithm exhibits a poor numerical stability behavior and the loss of orthogonality cannot ...

A new criterion for selective reorthogonalization in the modified Gram–Schmidt algorithm is proposed. We study its behavior in the presence of rounding errors. We give some counterexample matrices which prove that the standard criteria might fail. Through numerical experiments, we illustrate that our new criterion seems to be suitable also for the classical Gram– Schmidt algorithm with selectiv...

In this paper we study the parallel aspects of IMGS, Incomplete Modiied Gram-Schmidt preconditioner which can be used for ef-ciently solving sparse and large linear systems and least squares problems on massively parallel distributed memory computers. The performance of this preconditioning technique on this kind of architecture is always limited because of the global communication required for...