Abstract
Legendre polynomial (LP) has found extensive use in solutions of various physical phenomena. The roots of LP up to 44th order can be obtained using the popular and widely available MATLAB (7.5.0 R2007b) library function ‘roots’ which yields real roots only up to order 44. The solution is also found to have large errors due to limited precision in MATLAB. To obtain accurate roots of LP in MATLAB, it is very important to obtain accurate LP coefficients. It is possible that other mathematical software like Maple do not have this limitation. This article explores the roots of 44th-order LP used in Gaussian quadrature in MATLAB. The accuracy of higher-order LP roots has been improved using the variable precision integer (VPI) format in MATLAB. MATLAB’s ‘roots’ function and VPI method are also compared.
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Jatin, D., Muttanna, H.K., Sheshadri, T.S., Ramesh, N. (2014). Improved Accuracy of Higher-Order Legendre Polynomial Roots in MATLAB. In: Sridhar, V., Sheshadri, H., Padma, M. (eds) Emerging Research in Electronics, Computer Science and Technology. Lecture Notes in Electrical Engineering, vol 248. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1157-0_17
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DOI: https://doi.org/10.1007/978-81-322-1157-0_17
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