Abstract:
This article explores the computational intricacies of H. Rutishausers quotient-difference (Q-D) algorithm
and C programming code, a revolutionary advancement in polynomial analysis. Our specific focus is on cubic
polynomials featuring absolute, distinct non-zero real roots, emphasizing the algorithms distinctive capability
to simultaneously approximate all zeros independently of external data. Notably, it proves invaluable in diverse
domains, such as determining continuous fraction representations for meromorphic functions and serving as a
powerful tool in complex analysis for the direct localization of poles and zeros. To bring this innovation into
practice, the article introduces a meticulously crafted C language program, complete with a comprehensive
algorithm and owchart. Supported by illustrative examples, this implementation underscores the algorithms
robustness and effectiveness across various real-world scenarios.
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