PARALLEL PROCESSOR AND METHOD FOR SOLVING CHARACTERISTIC VALUE PROBLEM OF SYMMETRICAL MATRIX

摘要

PROBLEM TO BE SOLVED: To accurately and efficiently calculate a characteristic value or cheacteristic vector by a computer system which processes a characteristic value problem of a real symmetrical matrix. SOLUTION: A deforming means 1 generates a 2nd matrix by shifting diagonal elements of a 1st matrix of real symmetry byγ. A 1st parallel processing means 2 finds the characteristic valueλ' and the characteristic vector (v) of the 2nd matrix in parallel by a one-sided Jachobian method and a counting-back means 3 finds the characteristic valueλof the 1st matrix by subtractingγfromλ'. Even when the 1st matrix has two characteristic values which are different in only sign, they are shifted to obtain an accurate solution. Similarly, the diagonal elements are shifted to generate a positive-valued symmetrical matrix, which is decomposed by cholesky decomposition to make it possible to efficiently perform a tridiagonalizing process. Further, the elements of the tridiagonal matrix are shifted and deformed into a block bidiagonal matrix and then its simultaneous equations can be solved recursively.