This report presents a faster version of the polynomial recursive orthogonalization (PRO) algorithm, which is used in segmented image coding to generate orthonormal base functions on a non-rectangular discrete image. It shows that up to 25% of the oating point operations can be eliminated by using previously computed results; also, some orthogonalizations can be avoided altogether, because they...

A new inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tri-diagonal matrix on parallel computers is developed. The modified Gram-Schmidt orthogonalization is used in the classical inverse iteration. This algorithm is sequential and causes a bottleneck in parallel computing. In this paper, the use of the compact WY representation is proposed in the...

The representations currently used by local search and some evolutionary algorithms have the disadvantage that these algorithms are partially blind to “ridges” in the search space. Both heuristics search and gradient search algorithms can exhibit extremely slow convergence on functions that display ridge structures. A class of rotated representations are proposed and explored; these rotated rep...

This paper is concerned with a technique for solving Volterra integral equations in the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernel method, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series.An iterative method is given to obtain the approximate solution.The conver...

This paper is concerned with a technique for solving Volterra integro-dierential equationsin the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernelmethod, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series. An iterative method is given toobtain the...

The advancement of quantum computers undermines the security classical blockchain, necessitating either a post-quantum upgrade existing architecture or creation an inherently blockchain. Here we propose practically realizable model fully blockchain based on generalized Gram-Schmidt procedure utilizing dimensional lifting. In this model, information transactions stored in multi-qubit state are s...