We study the numerical approximation of a time dependent equation involving fractional powers of an elliptic operator L defined to be the unbounded operator associated with a Hermitian, coercive and bounded sesquilinear form on H 0 (Ω). The time dependent solution u(x, t) is represented as a Dunford Taylor integral along a contour in the complex plane. The contour integrals are approximated usi...

Matrix fixed-point iterations zn+1 = ψ(zn) defined by a rational function ψ are considered. For these iterations a new proof is given that matrix convergence is essentially reduced to scalar convergence. It is shown that the principal Padé family of iterations for the matrix sign function and the matrix square root is a special case of a family of rational iterations due to Ernst Schröder. This...

We propose a new technique for the mitigation of fail-stop failures and/or silent data corruptions (SDCs) within linear, sesquilinear or bijective (LSB) operations on M integer data streams (M ≥ 3). In the proposed approach, the M input streams are linearly superimposed to form M numerically entangled integer data streams that are stored in-place of the original inputs, i.e., no additional (aka...

in this paper we prove existence the common fixed point with different conditions for $alpha-psi$-contractive mappings. and generalize weakly zamfirescu map in to modified weakly zamfirescu map.