Read e-book online Tensor calculus PDF

By J. L. Synge

ISBN-10: 0486636127

ISBN-13: 9780486636122

Basic advent for starting pupil of absolute differential calculus and for these attracted to functions of tensor calculus to mathematical physics and engineering. issues contain areas and tensors; easy operations in Riemannian area, curvature of area, unique varieties of house, relative tensors, principles of quantity, more.

Show description

Read or Download Tensor calculus PDF

Similar analysis books

Read e-book online Risk-Based Reliability Analysis and Generic Principles for PDF

For a very long time, traditional reliability analyses were orientated in the direction of picking the extra trustworthy procedure and preoccupied with maximising the reliability of engineering structures. at the foundation of counterexamples notwithstanding, we display that deciding upon the extra trustworthy method doesn't inevitably suggest choosing the procedure with the smaller losses from mess ups!

Download e-book for kindle: Analysis and Topology in Nonlinear Differential Equations: A by Djairo G de Figueiredo, João Marcos do Ó, Carlos Tomei

This quantity is a suite of articles offered on the Workshop for Nonlinear research held in João Pessoa, Brazil, in September 2012. The impact of Bernhard Ruf, to whom this quantity is devoted at the celebration of his sixtieth birthday, is perceptible through the assortment by way of the alternative of issues and methods.

Additional info for Tensor calculus

Sample text

Hence we define the level number li of vertex i in the elimination tree to be the number of vertices on the chain joining the root and vertex i. The level numbers will be useful in setting up a mechanism for directly accessing the nonzeros in a row of H. We now provide a 6 x 6 example in Figures 11 and 12 to illustrate these ideas. It is easy to verify that the structures of its Householder matrix H and its triangular X X X A= X X X X X X X X X X Figure 11: Structure of the matrix A. factor R are as shown in Figure 12.

Since P APT is also symmetric and positive definite for any permutation matrix P, this means we can choose to reorder A symmetrically to reduce fill without regard to numerical stability and before the actual numerical factorization begins. These options, which are not normally available to us when A is a general indefinite matrix, have enormous practical implications. Since the ordering can be determined before the factorization begins, the locations of the fill suffered during the factorization can also be determined.

With P = n, the calculation of Ax and Ad requires n parallel steps rTd, dTAd, rTr requires log n parallel steps. >E do 26 So one iteration costs 2n + 3 log n + 4 steps. If p = n 2 we can do all the multiplications in Ax and Ad in parallel so one iteration is only 3 log n + 6 steps. 6 Preconditioning In practice on a sequential machine both Jacobi and Conjugate Gradients are preconditioned before use. In the Jacobi method this involves the use of either a matrix C or a matrix M where the equation becomes CAx = Cb or M- 1Ax M- 1b.

Download PDF sample

Tensor calculus by J. L. Synge


by John
4.4

Rated 4.60 of 5 – based on 14 votes