For any interpolatory ternary subdivision scheme with two-ring stencils for a regular triangular or quadrilateral mesh, we show that the critical Hölder smoothness exponent of its basis function cannot exceed log3 11(≈ 2.18266), where the critical Hölder smoothness exponent of a function f : R2 → R is defined to be ν∞(f) := sup{ν : f ∈ Lip ν}. On the other hand, for both regular triangular and ...

We present a parallel algorithm for solving triangular systems of linear equations on distributed-memory multiprocessor machines. The parallelism is achieved by partitioning the rows of the coefficient matrix in segments of a fixed size and distributing these sets in a wrap-around fashion among the processors, connected in a ring. The granularity of the algorithm is controlled by varying the se...

We prove that the Ricci flow equation for left invariant metrics on Lie groups reduces to a first order ordinary differential equation for a map Q : (−a, a) → UT , where UT is the group of upper triangular matrices. We decompose the matrix Rij of Ricci tensor coordinates with respect to an orthonormal frame field Ei into a sum 1 Rij + 2 Rij + 3 Rij + 4 Rij such that, for any Ei′ = U i i′Ei with...

A triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal are zero. Conversely a square matrix is called upper triangular if all the entries below the main diagonal are zero. [6] For a square matrix M , M−1 is the inverse matrix where M ×M−1 = I and I denotes the n× n identity matrix. We say that the problem siz...

The Schur method for computing a matrix square root reduces the matrix to the Schur triangular form and then computes a square root of the triangular matrix. We show that by using either standard blocking or recursive blocking the computation of the square root of the triangular matrix can be made rich in matrix multiplication. Numerical experiments making appropriate use of level 3 BLAS show s...