Review of Gram - Schmidt and Gauss ’ s Algorithm

ON THE CONTINUITY OF PROJECTIONS AND A GENERALIZED GRAM-SCHMIDT PROCESS

Let ? be an open connected subset of the complex plane C and let T be a bounded linear operator on a Hilbert space H. For ? in ? let e the orthogonal projection onto the null-space of T-?I . We discuss the necessary and sufficient conditions for the map ?? to b e continuous on ?. A generalized Gram- Schmidt process is also given.

Gauss elimination algorithm for interval matrix

Application of Schmidt rebound number for estimating rock strength under specific geological conditions

A literature review revealed that most of the empirical equations introduced for determination of the uniaxial compressive strength (UCS) of rocks based on the Schmidt hammer rebound number (N) are not sufficiently reliable mostly due to the relatively low coefficient of correlations. This is attributed to the fact that in most cases one formula is used for all types of rocks, altho...

Gram–Schmidt Process in Different Parallel Platforms

Important operations in numerical computing are vector orthogonalization. One of the well-known algorithms for vector orthogonalisation is Gram–Schmidt algorithm. This is a method for constructing a set of orthogonal vectors in an inner product space, most commonly the Euclidean space Rn. This process takes a finite, linearly independent set S = {b1, b2, ..., bk} vectors for k ≤ n and generates...

Robust Selective Gram-schmidt Reorthogonalization

A new criterion for selective reorthogonalization in the Gram-Schmidt procedure is given. We establish its comportment in presence of rounding errors when the criterion is used with modified Gram-Schmidt algorithm and show counter-example matrices which prove that standard criteria are not always valid. Experimentally, our criterion is fine also for the classical Gram-Schmidt algorithm with reo...