IN THIS PAPER, WE CONSIDER CONSTRUCTING OF PSEUDO-SYMMETRIC JACOBI MATRICES. WE DENOTE THE MATRIX OBTAINED BY KNOKING THE (M+1) TH ROW AND COLUMN OF THE MATRIX J BY JM+1. USING TWO SPECTRA, THE SPECTRUM OF PSEUDO- SYMMETRIC JACOBI MATRIX J AND SPECTRUM OF MATRIX JM+1, WE PROPOSE AN ALGORITHM FOR CONSTRUCTING THE ORIGINAL MATRIX J. WE GIVE CONDITIONS ON GIVEN SPECTRAL DATA FOR EXISTENCE AND UNIQUELY RECONSTRUCTION.

LET R BE A RING AND V BE A MATRIX VALUATION ON R, M (R) AND GL (R) WILL REPRESENT, AN ASSOCIATIVE RING WITH UNIT, THE SET OF ALL SQUARE MATRICES, AND THE SET OF INVERTIBLE MATRICES OVER R RESPECTIVELY.

IN THIS PAPER, WE DISCUSS THE ADAPTIVE JACOBI ITERATIVE METHOD WHICH USES P = I + S (A) + K (B) AS A PRECONDITIONER. WE PRESENT SOME COMPARISON THEOREMS, WHICH SHOW THE RATE OF CONVERGENCE OF THE NEW METHOD IS FASTER THAN THE BASIC METHOD. NUMERICAL EXAMPLE SHOW THE EFFECTIVENESS OF OUR ALGORITHM.

IN THIS ARTICLE, WE APPLY JACOBI POLYNOMIAL TO SOLVE RICCATI DIFFERENTIAL EQUATION OF FRACTIONAL ORDER. A GENERAL FORMULA FOR THE JACOBI OPERATIONAL MATRIX OF FRACTIONAL INTEGRAL OPERATOR IS CONSTRUCT. THE NUMERICAL RESULTS FOR THE EXAMPLES DEMONSTRATE THE EFFICIENCY OF THE PRESENT METHOD.

IN THIS PAPER, WE PRESENTS A COMPUTATIONAL TECHNIQUE FOR SOLUTION TO A CLASS OF SINGULAR BOUNDARY VALUE PROBLEMS ARISING IN PHYSIOLOGY. THE METHOD IS BASED UPON JACOBI PSEUDO SPECTRAL METHOD. NUMERICAL EXAMPLES ARE PRESENTED TO DEMONSTRATE THE VALIDITY AND APPLICABILITY OF THE METHOD, AND A COMPARISON IS MADE WITH EXISTING METHODS IN THE LITERATURE.