Wisdom E numerical PEVM methods. Mudrs A.E. Numerical methods for PEVM in Baseik, Fortran and Pascal. Brief abstract book
A Book Is The Best And The Oldest Way to Pass Knowledge Through Ages. More books. Appeared, More Information Had to Be Saved. TECHNICAL PROGRESS LEAD US TO electronic Books.And than - Electronic Libraries. Digital Library IS The Perfect Way to Collect Great Amount Of e-Books, Magazines, Articles, Scientific PublicationsWhich Provides Fast and Convenient Access to Necessary Information. Some Time Ago, IF You Needed Any Kind of Information, You Had to Go To public Library. And. find Book ON THE SHELVES. NowAdays Electronic Libraries Help US Not to Waste Our Time and Find Ebook As Quickly As Possible.
Download books. PDF, Epub.
Z-Library Is One of The Best and The Biggest electronic Libraries.. You can Find Everything You Want and download Books. for free, without charge. Our Free Digital Library Contains Fiction, Non-Fiction, Scientific Literature, Also All Kinds of Publications and So ON. Useful Search by Category Will Help You Not to Get Lost In Great Variety of E-Books. YOU CAN download Books. For Free in Any Suitable Format: IT CAN BE fB2, PDF, LIT, EPUB. IT IS Worth To Say That You Can Download Books Without Registry, without SMS and Very Quickly. Also, as you wish, it is possible to read Online.Search Books Online
If You Have Something To Share, You Can Add Book to Library. IT Will Make Z-Library Bigger and More Helpful for People. Z-Library Is The Best E-Books Search Engine.ON JULY 20, WE HAD THE LARGEST Server Crash in The Last 2 Years. Mostly The Data of The Books and Covers Were Damaged So Many Books Are Not Available for Download Now. Also, Some Services May Be Unstable (for example, Online Reader, File Conversion). Full Recovery of All Data Can Take Up To 2 Weeks! SO WE Came to Double The Download Limits for All Users Until The Problem is Completely resolved. Thanks for Your Understanding!
Progress: 90.4%
Restored
Books. Download Djvu books, PDF for free. Free digital library
A.E. Wise, numerical methods for PC ...
You can (program will celebrate yellow)
You can see a list of books on higher mathematics with sorting alphabetically.
You can see a list of books on top physics with sorting alphabet.
Free Download Book , volume 5.69 MB, format.djvu (Tomsk, 1991)
Ladies and gentlemen!! In order to download electronic publication files without "glitches", click on the underlined link with the file Right mouse button, Select Team "Save Target As ..." ("Save the object as ...") And save the electronic publication file to the local computer. Electronic publications are usually represented in Adobe PDF and DJVU formats.
Chapter 1. Transcendental Equations
1.1. Branch of roots
1.2. Dichotomy method
1.3. Horde method
1.4. Newton Method (Tangent Method)
1.5. Method of sequent
1.6. Method of simple iterations
Chapter 2. Problems of linear algebra
2.1. Gauss method with choosing the main element for solving Slava
2.2. Iterative methods solving Slava
2.3. Calculation of determinants
2.4. Calculation of the elements of the return matrix
2.5. Calculation of eigenvalues \u200b\u200bof matrix
Head 3. Interpolation of dependencies
3.2. Interpolation polynomial Lagrange
3.3. Interpolation Polin Nevton
3.4. . Replace interpolation to solve equations
3.5. Interpolation method for determining their own matrix values
3.6. Interpolation splines
Chapter 4. Method of the least squares
4.1. General algorithm
4.2. Power Basis
4.3. Basis in the form of classical orthogonal polynomials
4.4. Basis in the form of orthogonal polynomials of the discrete variable function
4.5. Linear version of MNC
4.6. Differentiation in approximation of MNA dependencies
Chapter 5. Definition of the Integral
5.1. Classification of methods
5.2. Methods of rectangles
5.3. A posteriori estimates of errors on Runge and Eitken
5.4. Traperation method
5.5. Simpson method
5.6. Calculation of integrals S. specified accuracy
5.7. Application of splines for numerical integration
5.8. Methods of the highest algebraic accuracy
5.9. Invalid integrals
5.10. Monte Carlo methods
Chapter 6. Cauchy Problem for Ordinary Differential Equations
6.1. Types of tasks for ordinary differential equations
6.2. Euler method
6.3. Second-order runge-kutta methods
6.6. Adams method
6.7. Gira method
Chapter 7. Boundary Tasks
7.1. The method of finite differences for linear boundary tasks
7.2. Footing method for boundary tasks
7.3. Boundary tasks for eigenvalues \u200b\u200bfor ordinary differential equations
7.4. The shooting method for the problem of eigenvalues
7.5. The final difference method for the task of eigenvalues
7.6. Boundary task for differential equation in private derivatives
Chapter 8. Unconditional Optimization of Functions
8.1. Golden section method
List of programs
1.1. Tablet method of root separation
1.2. Dichotomy method
1.3. Horde method
1.4. Newton Method
1.5. Newton Method in the Complex Area
1.6. Method of sequent
1.7. Method of simple iterations
2.1. Gauss method for Slava
2.2. Zeidel Method for Slava
2.3. Calculation of determinants in Gauss
2.4. Treatment of the matrix
2.5. Direct method for calculating your own matrix values
2.6. The iterative method of calculating the greatest value
3.1. Interpolation canonical polynomial
3.2. Polin Lagrange and its derivatives
3.3. Newton Polina and its derivatives
3.4. Parabola method
3.5. Interpolation method for calculating eigen matrix values
3.6. Interpolation splines
4.1. MNC with a power base
4.2. Matrix Gram with a Power Base
4.3. MNG with an arbitrary basis
4.4. MNA with orthogonal basis
4.5. Linear version of MNC
4.6. Calculation of derivatives
5.1. Method of medium rectangles
5.2. Traperation method
5.3. Simpson method
5.4. Simpson Method with Error Assessment
5.5. Spline quadrature
5.6. Gauss method with two nodes
5.7. Gaussian method with six nodes
5.8. Hermita Quadrature with Five Nodes
5.9. Monte Carlo method
6.1. Euler method
6.2. Second-order runge-kutta method with medium derivative correction
6.3. Second-order rung-kutta method with midpoint correction
6.4. Runge-Kutta fourth order method
6.5. Runge-Kutta Mersson
6.6. Adams method
6.7. Gira method
7.1. The method of finite differences for a linear boundary problem
7.2. Firing method for a linear boundary problem
7.3. The shooting method for the problem of eigenvalues
7.4. The final difference method for the task of eigenvalues
7.5. DRIKHLA problem for Laplace equation
8.1. Golden section method
8.2. Method of coordinate descent
8.3. The method of gradient descent
Brief abstract book
The main methods and algorithms of computational mathematics are presented. The specialists of their software implementation on personal computers are considered. Descriptions and listings of about 150 programs in Baysik, Fortran and Pascal are given. Parallel texts of programs in three languages \u200b\u200bwill be useful to readers owning one of them for the practical development of the other two. For scientific and engineering and technical workers of various specialties; May be useful to students of universities studying programming.
Personal computers (PC) are widely introduced into science and equipment, education, management activities, technological processes, etc. The effectiveness of the application of the PEVM is primarily associated with software, both with the presence of ready-made packages of system and books of health programs and with the ability of the user to adapt them to solve specific tasks.
Mathematical modeling of processes and phenomena in different areas Science and technology is one of the main ways to obtain new knowledge and technological solutions. For implementation mathematical modeling The researcher, regardless of its specialty, should know a certain minimum set of algorithms of computing mathematics, as well as possess the methods of their software implementation on the PC. Such knowledge and skills are also necessary when using ready-made software packages, otherwise the planning of the computational experiment and the interpretation of its results will be difficult.
Currently, extensive literature on calculation methods, programming on algorithmic languages. However, a relatively small number of publications combines these two directions.
From books on computational mathematics of universal content intended for individuals who are not experts in this area, we note in which the availability of the presentation is combined with sufficient severity and the practical orientation of the algorithms outlined. Popularity among researchers and engineers is manifested in numerous references to it in scientific publications related to the computational experiment in mathematical modeling in various fields of science and technology. IN last years A number of books were published, where a wide range of methods and algorithms is presented, as well as works in which separate sections of computing mathematics are more in-depth.
Among the books that combine the presentation of computational algorithms with their implementation in the language of Baysik, we note, and in Fortran -. Similar work with programs in Pascal, where systematically methods of computing mathematics would be presented, the author is not known to the author.
When working on PEVM, BASIC, FORTRAN and Pascal programming languages \u200b\u200bare widely used, each of which has certain advantages and disadvantages.
Thus, there are weak structure, a relatively slow speed of performing computing algorithms, the possibility of side effects due to the "overlapping" of variables in subroutines. But at the same time, Beysicik's programs are distinguished by readability and disorder, shortness and availability of the dialogue mode, ease of direct additions and corrections without using editors and re-compile programs. Such features allow you to use a base for the implementation of relatively simple algorithms, as well as when checking and debugging individual fragments of complex algorithms and programs.
Fortran is distinguished by insufficient structure, the presence of a plurality of archaisms, which remained from the time of the first computer, non-controlling ads and the introduction of new variables by default. But at the same time, a rich experience of applying the language has been accumulated and extensive software packages have been created for solving applied tasks, systematic mathematical support and, in particular, optimizing compilers for use of Fitran on different computers are developed. Scientists and engineers Ford attracts simplicity of working with complex variables and functions.
In training Programming and practice, PCHM is now widely used and tongue Pascal due to its structure, clear and unambiguous grammar, convenience of working with file structures. However, some cumbersome records of programs due to the need to describe all the objects used, the lack of development of problematic mathematical support, the lack of optimizing compilers on some PEVM are an obstacle to the tasks of mathematical modeling in Pascal.
Due to the specified features of programming languages \u200b\u200bat different stages of solving applications, it is advantageous to use different languages \u200b\u200bor combine them at one stage when programming parts of one task. Since each language has its own set of funds for the software implementation of algorithms, the "literal" translation of programs from one language to another is not always possible. The same algorithm must be recorded in each programming language using its visual funds. There is a situation similar to the translation of the text from one natural language to another.
In the proposed book, classical methods of computing mathematics are illustrated by parallel programs in Baysik, Fortran and Pascal. A total of about 150 completed programs are given. The programs were made up so that they were easy to read and upgrade, to take as a basis when developing software complexes. Without special difficulties, the program can be adapted to other TEVM types. In programs where it is possible without prejudice to readability and simplicity, the number of variables used and operators is minimized, and the text of each section provides a summary of the computing method and the task used for example, the information necessary for the transition of the method of the method to the program is given, a generalized block is considered. -Shem program. More detailed descriptions are given to the programs in the Baysik language, where attention is drawn to "pitfalls", the logic of using certain structures is explained. In explanations of the programs in Fortran and Pascal languages, attention is drawn only to distinctive features from the programs on Basic.
The reader who owns one of the named programming languages, with the help of the proposed book will be able to almost master the other two.
The first chapter discusses the methods and algorithms of separation and refining the roots of transcendental equations with parameters. As examples, equations containing special functions of mathematical physics are used, among which Bessel functions, elliptic integrals, logarithmic derivative of the U-function, Fresnel integrals, probability integral. Subprograms for calculating these functions can be used as independent separately from the subroutines for solving equations. The first chapter shows a method for implementing computing with complex variables on different languages Programming.
The second chapter discusses the exact and iterative methods for solving systems of linear algebraic equations, calculating the determinants, inverse matrices, finding your own matrices.
The third chapter provides algorithms and programs for interpolation by polynomials and splines. Practical methods of numerical differentiation of approximating functions are considered, the use of interpolation to solve equations and calculating the eigenvalues \u200b\u200bof matrices.
In the fourth chapter, various variants of the method of least squares used to process experimental data, smoothing and differentiation of dependencies, reduction of numerical information. The methods of the method with a power base, the basis in the form of classical orthogonal polynomials and polynomials of the discrete variable, linear variant of the method are given.
The fifth chapter contains the presentation of the most common ways to calculate certain integrals and programs implementing interpolation methods, the methods of the highest algebraic accuracy and statistical tests.
The sixth chapter discusses the algorithms for solving the Cauchy problem for the system of ordinary differential equations. Programs of runge-kutt methods of different orders are given, among which there is a method of a method with an automatic choice of integration step. The methods of Adams and the prediction gir type are selected from multipoint methods.
The seventh chapter is devoted to the methods of solving boundary problems for ordinary differential equations and equations in private derivatives. Programs of shooting and final difference methods are offered for boundary tasks and tasks to eigenvalues. As an example of the tasks of the last class, the problem of the propagation of electromagnetic waves in the coaxial waveguide structure is considered.
In the eighth chapter, programs for elementary methods of unconditional minimization of the function of one and many variables have been developed.
The proposed book is designed for scientific and engineering and technical workers who are not experts in the field of programming and computing mathematics wishing to put and solve applied tasks using PC. The author does not pretend to complete the coverage and depth of the presentation of the selected methods, the material considered should be considered an introduction to the immense world of computational mathematics.
Tomsk: MP "Rasco", 1991. - 272 p.
The main methods and algorithms of computational mathematics are presented. The features of their program implementation on personal computers are considered. Detailed descriptions and listings of about 150 programs in Baysik, Fortran and Pascal are given. Parallel texts of programs in three languages \u200b\u200bwill be useful to readers owning one of them for the practical development of the other two.
_Transgenerate equations.
Branch of roots.
Dichotomy method.
Horde method.
Newton Method (tangent method).
The method of sequential.
Method of simple iterations.
_Alls of linear algebra.
Gaycca method with choosing the main element.
Iterative methods solving Slava.
Calculation of determinants.
Calculation of elements of the return matrix.
Calculation of own values \u200b\u200bof matrices.
_ Interpolating dependencies.
Interpolation canonical polynomial.
Interpolation polynomial Lagrange.
Interpolation Newton's interpolation.
The use of interpolation to solve equations.
Interpolation method for determining their own matrix values.
Interpolation splines.
_Least square method.
General algorithm.
Power base.
Basis in the form of classical orthogonal polynomials.
Base in the form of orthogonal polynomials of the discrete variable function.
Linear version of MNC.
Differentiation in approximation of MNA dependencies.
_Other integrals.
Classification of methods.
Methods of rectangles.
A posteriori estimates of errors on Runge and Eitken.
Method of trapezium.
Simpson method.
Calculating integrals with a given accuracy.
Apply splines for numerical integration.
Methods of the highest algebraic accuracy.
Invalid integrals.
Methods Monte Carlo.
_ Cauchy for ordinary differential equations.
Type types for ordinary differential equations.
Euler method.
Second-order runge-kutta methods.
Fourth-order runge-kutta method.
Runge-Kutta-Merson.
Adams method.
Gear method.
_Round tasks.
The finite difference method for linear boundary tasks.
Firing method for boundary tasks.
Boundary tasks for eigenvalues \u200b\u200bfor ordinary differential equations.
The shooting method for the task to the eigenvalue.
The finite difference method for the task to the eigenvalues.
The boundary problem for the differential equation in private derivatives.
_Bezing optimization of functions.
Golden section method.
The method of coordinate descent.
The method of gradient descent. It may be interesting to the book similar to the structure:
PAO Y.C. Engineering Analysis: Interactive Methods and Programs with Fortran,
QuickBasic, Matlab, and Mathematica
