The Student edition of MATLAB student user guide
The Student edition of MATLAB student user guide
ACM Transactions on Mathematical Software (TOMS)
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
Principles for Testing Polynomial Zerofinding Programs
ACM Transactions on Mathematical Software (TOMS)
Computation of approximate polynomial GCDs and an extension
Information and Computation
Polynomial root finding using iterated Eigenvalue computation
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
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Conventional numerical methods for finding multiple roots of polynomials are inaccurate. The accuracy is unsatisfactory because the derivatives of the polynomial in the intermediate steps of the associated root-finding procedures are eliminated. Engineering applications require that this problem be solved. This work presents an easy-to-implement method that theoretically completely resolves the multiple-root issue. The proposed method adopts the Euclidean algorithm to obtain the greatest common divisor (GCD) of a polynomial and its fast derivative. The GCD may be approximate because of computational inaccuracy. The multiple roots are then deflated into simple ones and then determined by conventional root-finding methods. The multiplicities of the roots are accordingly calculated. A detailed derivation and test examples are provided to demonstrate the efficiency of this method.