Accurate SVDs of polynomial Vandermonde matrices involving orthonormal polynomials

Linear Algebra and Its Applications

Volumn 417, Issue 2-3, 2006, Pages 382-396

  Demmel, James ^a   Koev, Plamen ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

High relative accuracy; Orthogonal polynomial; Singular value decomposition; Vandermonde matrix

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; POLYNOMIALS; PROBLEM SOLVING;

HIGH RELATIVE ACCURACY; ORTHOGONAL POLYNOMIALS; SINGULAR VALUE DECOMPOSITION; VANDERMONDE MATRIX;

MATRIX ALGEBRA;

EID: 33746238438     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2005.09.014     Document Type: Article

References (16)

1. In: Abramowitz M., and Stegun I. (Eds). Handbook of Mathematical Functions. NBS, Appl. Math. Ser. vol. 55 (1965), US Government Printing Office, Washington, DC
2. Demmel J. On condition numbers and the distance to the nearest ill-posed problem. Numer. Math. 51 3 (1987) 251-289
3. Demmel J. Accurate singular value decompositions of structured matrices. SIAM J. Matrix Anal. Appl. 21 2 (1999) 562-580
4. Demmel J., Gu M., Eisenstat S., Slapničar I., Veselić K., and Drmač Z. Computing the singular value decomposition with high relative accuracy. Linear Algebra Appl. 299 1-3 (1999) 21-80
5. Demmel J., and Kahan W. Accurate singular values of bidiagonal matrices. SIAM J. Sci. Statist. Comput. 11 5 (1990) 873-912
6. Demmel J., and Koev P. Necessary and sufficient conditions for accurate and efficient rational function evaluation and factorizations of rational matrices. Structured Matrices in Mathematics, Computer Science, and Engineering, II (Boulder, CO, 1999). Contemp. Math. vol. 281 (2001), Amer. Math. Soc., Providence, RI 117-143
7. Gautschi W. Construction of Gauss-Christoffel quadrature formulas. Math. Comp. 22 (1968) 251-270
8. Gautschi W. The condition of Vandermonde-like matrices involving orthogonal polynomials. Linear Algebra Appl. 52/53 (1983) 293-300
9. Gautschi W. Is the recurrence relation for orthogonal polynomials always stable?. BIT 33 (1993) 277-284
10. Gautschi W. Orthogonal polynomials: applications and computation. Acta Numerica (1996) 45-119
11. Higham N.J. Accuracy and Stability of Numerical Algorithms. second ed. (2002), SIAM, Philadelphia
12. The MathWorks, Inc., Natick, MA. MATLAB Reference Guide, 1992.
13. Priest D. Algorithms for arbitrary precision floating point arithmetic. In: Kornerup P., and Matula D. (Eds). Proceedings of the 10th Symposium on Computer Arithmetic (1991), IEEE Computer Society, Grenoble, France 132-145
14. Schönhage A., and Strassen V. Schnelle Multiplikation grosser Zahlen. Computing (Arch. Elektron. Rechnen) 7 (1971) 281-292
15. Szegö G. Orthogonal Polynomials (1967), American Mathematical Society
16. Wolfram S. Mathematica: A System for Doing Mathematics by Computer (1988), Addison-Wesley, Reading, MA