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Numerical Recipes in Fortran 77: The Art of Scientific by William H. Press, Brian P. Flannery, Saul A. Teukolsky,

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By William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling

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Additional info for Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed. (Fortran Numerical Recipes 1)

Example text

In programming, it is the program user. Now, you may object that the target of communication of a program is not a human but a computer, that the program user is only an irrelevant intermediary, a lackey who feeds the machine. This is perhaps the case in the situation where the business executive pops a diskette into a desktop computer and feeds that computer a black-box program in binary executable form. The computer, in this case, doesn’t much care whether that program was written with “good programming practice” or not.

Roughly speaking, the machine accuracy m is the fractional accuracy to which floating-point numbers are represented, corresponding to a change of one in the least significant bit of the mantissa. Pretty much any arithmetic operation among floating numbers should be thought of as introducing an additional fractional error of at least m . This type of error is called roundoff error. It is important to understand that m is not the smallest floating-point number that can be represented on a machine.

At the other end of the spectrum, one seems just as often to encounter linear problems which, by their underlying nature, are close to singular. In this case, you might need to resort to sophisticated methods even for the case of N = 10 (though rarely for N = 5). 6) is a technique that can sometimes turn singular problems into nonsingular ones, in which case additional sophistication becomes unnecessary. 2) Here the raised dot denotes matrix multiplication, A is the matrix of coefficients, and b is the right-hand side written as a column vector,     a11 a12 .

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