Two method for computation of the spectra certain infinite graphs are suggested. The first one can be viewed as a reversed Gram--Schmidt orthogonalization procedure. It relies heavily on spectral theory Jacobi matrices. second is related to Schur complement block A number examples including with tails, chains cycles and ladders worked out in detail.

Abstract Multi-spectral CT (MSCT) is increasingly used in industrial non-destructive testing and medical diagnosis because of its outstanding performance like material distinguishability. The process obtaining MSCT data can be modeled as a nonlinear system the basis decomposition comes down to inverse problem system. For different spectra data, geometric inconsistent parameters cause geometrica...

K e y w o r d s N u m e r i c a l linear algebra, QR factorization, Gram-Schmidt orthogonalization, Reorthogonalization, Rounding error analysis. 1. I N T R O D U C T I O N Scientific comput ing and ma themat i ca l models in engineering are becoming increasingly dependent upon development and implementa t ion of efficient paral le l a lgor i thms on modern high performance computers . Numerica...

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...