C语言科学计算：线性代数方程求解实战

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"C程序数值试验大全Solution of Linear Algebraic EquationsThe Art of Scientific Computing" 这篇资源主要关注的是使用C语言进行科学计算，特别是数值方法在解决线性代数方程组中的应用。"Numerical Recipes in C: The Art of Scientific Computing" 是一本经典著作，第二版提供了关于插值、外推以及其他数值计算技术的详细指南。在C编程中，程序的组织和控制结构是基础且至关重要的部分。"1.1 Program Organization and Control Structures" 这一章节强调了这一点。书中可能涵盖了如何设计高效、可读性强的代码结构，包括基本的控制流语句（如if-else，for，while循环），以及函数的使用来模块化代码。这些结构使得程序员能够有效地控制程序的执行顺序，实现条件判断和迭代计算。 Kernighan和Ritchie的《C Programming Language》被提及，这是一本经典教材，通常被称为K&R，是学习C语言的标准参考书。书中可能提到了早期的“传统”C语言，而后续版本则遵循了ANSI C标准，这是C语言的正式规范。此外，资源中还引用了Meeus的《Astronomical Formulas for Calculators》，这表明除了基础的数值计算，该书可能还涉及了专门用于天文学计算的算法。这部分内容可能包含了一些天文计算中的数值方法，比如时间转换、天体位置计算等。在科学计算中，程序的组织和控制结构对于处理复杂的数学问题至关重要，如线性代数方程组的求解。这通常涉及到矩阵运算，例如高斯消元法、LU分解、QR分解或迭代方法（如Gauss-Seidel或Jacobi方法）。这些方法在解决实际问题时，如物理模拟、工程计算、数据拟合等领域都有广泛应用。这本书深入浅出地介绍了使用C语言进行数值计算的实践技巧，包括基本的编程原则和特定于科学计算的算法。无论是对初学者还是经验丰富的程序员，都是一个宝贵的资源，帮助他们理解和实现高效的数值计算解决方案。

1.1 Program Organization and Control Structures

Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)

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modularization and encapsulation become important programming concepts, the

general idea being that program units should interact with one another only through

clearly deﬁned and narrowly circumscribed interfaces. Good modularizationpractice

is an essential prerequisite to the success of large, complicated software projects,

especially those employing the efforts of more than one programmer. It is also good

practice (if not quite as essential) in the less massive programming tasks that an

individual scientist, or reader of this book, encounters.

Some computer languages, such as Modula-2 and C++, promote good modular-

ization with higher-level language constructs absent in C. In Modula-2, for example,

functions, type deﬁnitions, and data structures can be encapsulated into “modules”

that communicate through declared public interfaces and whose internal workings

are hidden from the rest of the program

[4]

.IntheC++ language, the key concept

is “class,” a user-deﬁnable generalization of data type that provides for data hiding,

automatic initializationof data, memory management, dynamic typing, and operator

overloading (i.e., the user-deﬁnable extension of operators like + and * so as to be

appropriate to operands in any particular class)

[5]

. Properly used in deﬁning the data

structures that are passed between program units, classes can clarify and circumscribe

these units’ public interfaces, reducing the chances of programming error and also

allowing a considerable degree of compile-time and run-time error checking.

Beyond modularization, though depending on it, lie the concepts of object-

oriented programming. Here a programming language, such as C++ or Turbo Pascal

5.5

[6]

, allows a module’s public interface to accept redeﬁnitions of types or actions,

and these redeﬁnitions become shared all the way down through the module’s

hierarchy (so-called polymorphism). For example, a routine written to invert a

matrix of real numbers could — dynamically, at run time — be made able to handle

complex numbers by overloading complex data types and corresponding deﬁnitions

of the arithmetic operations. Additional concepts of inheritance (the ability to deﬁne

a data type that “inherits” all the structure of another type, plus additional structure

of its own), and object extensibility (the ability to add functionality to a module

without access to its source code, e.g., at run time), also come into play.

We have not attempted to modularize, or make objects out of, the routines in

thisbook, for at least two reasons. First,the chosen language, C, does not really make

this possible. Second, we envision that you, the reader, might want to incorporate

the algorithms in this book, a few at a time, into modules or objects with a structure

of your own choosing. There does not exist, at present, a standard or accepted set

of “classes” for scientiﬁc object-oriented computing. While we might have tried to

invent such a set, doing so would have inevitably tied the algorithmic content of the

book (which is its raison d’ˆetre) to some rather speciﬁc, and perhaps haphazard, set

of choices regarding class deﬁnitions.

On the other hand, we are not unfriendly to the goals of modular and object-

oriented programming. Within the limits of C, we have therefore tried to structure

our programs to be “object friendly.” That is one reason we have adopted ANSI

C with its function prototyping as our default C dialect (see §1.2). Also, within

our implementation sections, we have paid particular attention to the practices of

structured programming, as we now discuss.

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