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 ...

This essay looks at the historical significance of five APS classic papers that are freely available online: Murdaugh HV Jr, Schmidt-Nielsen B, Doyle EM, and O’Dell R. Renal tubular regulation of urea excretion in man. J Appl Physiol 13: 263–268, 1958. (http://jap.physiology.org/cgi/reprint/13/2/263) Schmidt-Nielsen B. Renal tubular excretion of urea in kangaroo rats. Am J Physiol 170: 45–56, 1...

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...

GPS radio occultation with CHAMP: monitoring of climate change parameters T. Schmidt, S. Heise, J. Wickert, G. Beyerle, and C. Reigber GeoForschungsZentrum Potsdam, Department 1: Geodesy and Remote Sensing, Potsdam, Germany Received: 20 September 2004 – Accepted: 27 October 2004 – Published: 1 December 2004 Correspondence to: T. Schmidt ([email protected]) © 2004 Author(s). This work is l...

The preparation of substituted pyrrolizines through the Schmidt reaction of acyl chlorides with alkyl azides has been realized. Intramolecular capture of the isocyanate ion and N-acyliminium ion intermediates from the Schmidt process with alkene or alkyne units was achieved, and the efficiency of the conversion with respect to ring construction and bond formation was demonstrated.

We prove a conjecture of G.A. Margulis on the abundance of certain exceptional orbits of partially hyperbolic flows on homogeneous spaces by utilizing a theory of modified Schmidt games, which are modifications of (α, β)-games introduced by W. Schmidt in mid-1960s.

In this paper, after collecting the rock samples from eight mines and one high way slope, the tests for determination of dry density, Uniaxial Compressive Strength, tensile Strength (Brazilian Test), elastic modulus, Schmidt hammer rebound number have been done on samples. In addition, in order to calculating the mean size of rock grains, quartz content, hardness and abrasivity, a thin sections...

In this paper, we use the method of characteristics to study singularities in the flow of a parameterized family of extremals for an optimal control problem. By means of the Lyapunov–Schmidt reduction a characterization of fold and cusp points is given. Examples illustrate the local behaviors of the flow near these singular points. Singularities of fold type correspond to the typical conjugate ...