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- W144670873 abstract "Publisher Summary This chapter discusses computer demonstration packages for standard problems of numerical mathematics. There are packages programmed for the solution of linear systems, Eigen problems, zeros of polynomials, evaluation of arbitrary arithmetic expressions, and differential equations. The computed bounds are of high accuracy. In many cases, the left and right bounds of the resulting intervals are adjacent in the floating-point screen, that is, the bounds are best possible. It is called least significant bit accuracy (lsba). The presented examples show that even for ill-conditioned problems, such as a linear system with the Hilbert 15 × 15 matrix, bounds with the lsba-property are computable. The programming language is a PASCAL extension called PASCAL-SC. The language extension PASCAL-SC allows the user to develop programs in a simple, easy to read manner. This is achieved especially by the general function concept and the possibility of user defined operators with arbitrary result type. The correctness of the computed bounds as well as the existence and the uniqueness of the solution within these bounds are verified automatically by the computer without any effort on the part of the user." @default.
- W144670873 created "2016-06-24" @default.
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- W144670873 date "1983-01-01" @default.
- W144670873 modified "2023-09-25" @default.
- W144670873 title "COMPUTER DEMONSTRATION PACKAGES FOR STANDARD PROBLEMS OF NUMERICAL MATHEMATICS" @default.
- W144670873 doi "https://doi.org/10.1016/b978-0-12-428660-3.50009-4" @default.
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