In this paper we report an eeective parallelisation of the House-holder routine for the reduction of a real symmetric matrix to tri-diagonal form and the QL algorithm for the diagonalisation of the resulting matrix. The Householder algorithm scales like N 3 =P + N 2 log 2 (P) and the QL algorithm like N 2 + N 3 =P as the number of processors P is increased for xed problem size. The constant par...

Abstract Pattern Search is a family of gradient-free direct search methods for numerical optimisation problems. The characterising feature pattern the use multiple directions spanning problem domain to sample new candidate solutions. These compose matrix potential moves, that pattern. Although some fundamental studies theoretically indicate various can be used, selection remains an unaddressed ...

We present a complete basis of multi-trace multi-matrix operators that has a diagonal two point function for the free matrix field theory at finite N . This generalises to multiple matrices the single matrix diagonalisation by Schur polynomials. Crucially, it involves intertwining the gauge group U(N) and the global symmetry group U(M) with Clebsch-Gordan coefficients of symmetric groups Sn. Wh...

Atom centred ab initio Hartree-Fock is introduced for periodic systems with helical symmetry. Such a structure is decomposed as a product of two crystal sub-groups, one of which being cyclic. This enables the Fock matrix of a finite cluster of cells to be Fourier transformed into a block diagonal form. The diagonalisation is performed on the sub-matrices and the mean field experienced by the ce...

We provide a library to facilitate the implementation of new models in codes such as matrix element and event generators or codes for computing dark matter observables. The library contains a SLHA reader routine as well as diagonalisation routines. This library is also available in CalcHEP, micrOMEGAs and LanHEP.

Given a matrix pseudodifferential operator on smooth manifold, one may be interested in diagonalising it by choosing eigenvectors of its principal symbol manner. We show that diagonalisation is not always possible, the whole cotangent bundle or even single fibre. identify global and local topological obstructions to examine physically meaningful examples demonstrating all possible scenarios can...

Based on an explicit diagonalisation of Abel’s integral operator, we give an inversion of the plane Radon transformation R(f)(p, θ) = ∫ {x cos(θ)+y sin(θ)=p} f(x, y) ds by diagonalising explicitly R̃(f)(r, φ) = R(f(r, φ)/r). We calculate the spectrum and the kernel of R̃.