On diagonalization in map(M,G)

On Diagonalization in Map(M,G)

Motivated by some questions in the path integral approach to (topological) gauge theories, we are led to address the following question: given a smooth map from a manifold M to a compact group G, is it possible to smoothly ‘diagonalize’ it, i.e. conjugate it into a map to a maximal torus T of G? We analyze the local and global obstructions and give a complete solution to the problem for regular...

Remarks on Recursion vs. Diagonalization

Results are presented which show precise ways in which recursion rests on very simple computational bases which do not support diagonalization. A method based on recursion and making no use of diagonalization is given for proving lower bounds on computational complexity. Thus the intractability of computational problems such as Presburger arithmetic does not depend on diagonalization. This rese...

Diagonalization methods in PARSEC ∗

The Pseudopotential Algorithm for Real-Space Electronic Calculations (PARSEC) is a software package written by a team consisting of materials scientists and computer scientists over approximately one decade. During this period, the algorithms used in PARSEC have undergone a series of improvements. This paper reviews the nature of the eigenvalue problems encountered in solving the Kohn-Sham equa...

Diagonalization in Parallel Space

Matrix diagonalization is an important component of many aspects of computational science. There are a variety of algorithms to accomplish this task. Jacobi’s algorithm is a good choice for parallel environments. Jacobi’s algorithm consists of a series of matrix plane rotations, the ordering of which can dramatically affect performance. We show a new ordering which cuts the number of necessary ...

Diagonalization in proof complexity