By Daoqi Yang

This publication is meant to be a simple, concise, yet fairly whole, introduc­ the ISO/ANSI C++ programming language with distinctive empha­ tion to sis on object-oriented numeric computation for college kids and execs in technology and engineering. the outline of the language is platform­ self sufficient. therefore it applies to various working platforms resembling UNIX, Linux, MacOS, home windows, and DOS, so long as a customary C++ compiler is provided. The prerequisite of this publication is ordinary wisdom of cal­ culus and linear algebra. although, this prerequisite is hardly ever precious if this e-book goes for use as a textbook for instructing C++ and the entire sections on numeric tools are skipped. Programming adventure in an­ different language similar to FORTRAN, C, Ada, Pascal, Maple, or Matlab will surely support, yet isn't really presumed. All C++ good points are brought in an effective way via suggestions corresponding to services, complicated numbers, vectors, matrices, and integrals, that are wide-spread to each pupil in technology and engineering. within the ultimate bankruptcy, complex positive factors that aren't present in FORTRAN, C, Ada, or Matlab, are illustrated within the context of iterative algorithms for linear structures corresponding to the preconditioned conjugate gradient (CG) approach and generalized minimal residual (GMRES) procedure. wisdom of CG, GMRES, and preconditioning options isn't presumed and they're ex­ plained intimately on the algorithmic level.

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It must be declared as usual in one and only one file: double x; II dec lare i t as usual i n one of the f iles It is this statement that creates an object and allocates space for x . ) External variables never disappear; they exist t hroughout the execution life of the program. To improve the modularity and readability of a program, the use of external variables should be kept to the minimum. 8) should not change an external variab le within its body rather than through its parameter list or return value.

Notice that, to save one bit of memory, the leading bit 1 in the fractional part is not stored. It is usually called the hidden bit. The exponent m takes values in the closed interval [-127,128]. However, m = -127 is reserved for ±O, and m = 128 for ±oo (if b: = b2 = ... = b23 = 1) and NaN (otherwise). Thus the exponent of a nonzero machine number must be in the range -126 ~ m ~ 127. 4 x 1038 (corresponding to b, = 1 for i = 1,2, . ,23 , and m = 127). 798 x 10308 • It can be shown (see [CK99, KC96]) that for any nonzero real number x and its floating point machine representation x (assuming x is within the range of the computer and thus no overflow or underflow occurs), there holds x-xl ~ -x- l epsilon, in the case of chopping, and x-xi -x- I 1 epsilon, ~ "2 in the case of rounding to the nearest machine number .

A temporary storage tmp is used to store fe before the updating and assign the stored value to fp after updating, getting ready for the next iteration. Notice that the integer fe is converted into long double before the division [c] fp is performed, since otherwise the result would be just an integer. This program works fine except the output may look messy. width(2); cout « "u'": II II previous Fibonacci number current Fibonacci number II output in a space of 2 chars 46 2. width(2); cout « n; cout.

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