High-accurate numerical method for integral equations of the first kind under multiple-precision arithmetic

Theoretical and Applied Mechanics Japan

Volumn 52, Issue , 2003, Pages 193-204

  Fujiwara, Hiroshi ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

MULTIPLE-PRECISION ARITHMATIC; NUMERICAL COMPUTATIONS; NUMERICAL INTEGRATION FORMULAE; SPECTRAL COLLOCATION METHOD;

COMPUTATIONAL METHODS; ERROR ANALYSIS; INTEGRAL EQUATIONS; INTERPOLATION; INVERSE PROBLEMS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PRECISION ENGINEERING; SPECTRUM ANALYSIS;

NUMERICAL METHODS;

EID: 21244464705     PISSN: 13480693     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Article

References (12)

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2. BAUMEISTER, J.: Stable Solution of Inverse Problems. F. Vieweg (1987).
3. FUJIWARA, H.: Design of multiple-precision arithmetic environment and its application to numerical computations of ill-posed problems. Graduate School of Informatics, Kyoto University (2000). Master Thesis (In Japanese).
4. FUJIWARA, H. and ISO, Y.: Numerical challenge to ill-posed problems by fast multiple-precision system. Theoretical and Applied Mechanics 50 (2001), 419-424.
5. IEEE standard for binary floating-point arithmetic : ANSI/IEEE std 754-1985 (1985).
6. Reprinted in SIGPLAN 22 (1987), 9-25.
7. IMAI, H. and TAKEUCHI, T.: Some advanced applications of the spectral collocation method. GAKUTO Internat. Ser. Math. Sci. Appl. 17 (2002), 323-335.
8. Iso, Y., FUJIWARA, H. and SAITO, K.: Numerical computations for ill-conditioned problems by multiple-precision systems. Mathematical Modeling and Numerical Simulation in Continuum Mechanics, Lecture Notes in Computational Science and Engineering 19 (2001), 185-194.
9. KRESS, R.: Linear Integral Equations (1st Ed.). Springer-Verlag (1989).
10. KRESS, R.: Numerical Analysis. Springer-Verlag (1998).
11. MIKHLIN, S. G. and SMOLITSKIY, K. L.: Approximate Methods for Solution of Differential and Integral Equations. American Elsevier (1967).
12. WILKINSON, J. H. and REINSCH, C.: Handbook for Automatic Computation, Volume 2, Linear Algebra. Springer-Verlag (1971).