A method for solving nonlinear polynomial equations is given which avoids theappearance of redundant factors as in the previous characteristic set method developed bythe present author. The new method seems thus to be...A method for solving nonlinear polynomial equations is given which avoids theappearance of redundant factors as in the previous characteristic set method developed bythe present author. The new method seems thus to be of much higher efficiency than theprevious one. It has the further advantage that numerical data may be inserted at willeither at the outset or during the procedure so far removal of factors by divisions may beavoided.展开更多
The generalized Sturm sequence is used to determine the number of real roots of a polynomialf(x) subject toh(x)>0 whereh(x) is another polynomial. To construct this sequence, the original procedure is almost the sa...The generalized Sturm sequence is used to determine the number of real roots of a polynomialf(x) subject toh(x)>0 whereh(x) is another polynomial. To construct this sequence, the original procedure is almost the same as Euclidean algorithm, so it is terribly inefficient for polynomials with symbolic coefficients. A new method is developed instead, which succeeds in avoiding the high computational complexity caused by the division algorithm.展开更多
基金The present project is partially supported by NSFC Grant JI85312.
文摘A method for solving nonlinear polynomial equations is given which avoids theappearance of redundant factors as in the previous characteristic set method developed bythe present author. The new method seems thus to be of much higher efficiency than theprevious one. It has the further advantage that numerical data may be inserted at willeither at the outset or during the procedure so far removal of factors by divisions may beavoided.
文摘The generalized Sturm sequence is used to determine the number of real roots of a polynomialf(x) subject toh(x)>0 whereh(x) is another polynomial. To construct this sequence, the original procedure is almost the same as Euclidean algorithm, so it is terribly inefficient for polynomials with symbolic coefficients. A new method is developed instead, which succeeds in avoiding the high computational complexity caused by the division algorithm.
