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Basic scientific subroutines

Author: Ruckdeschel, F. R. Publisher: Byte, 1981. ; McGraw-Hill, 1981.Language: EnglishDescription: Various pagings ; 24 cm.Type of document: BookBibliography/Index: Includes bibliographical references and indexContents Note: Vol. 1, ISBN 0-07-054201-5, 316 p.; vol. 2, ISBN0-07-054203-3, 790 p.
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print QA76.6 .R83 1981 Vol.1
(Browse shelf)
001159478
Available 001159478
Book Europe Campus
Main Collection
Print QA76.6 .R83 1981 Vol.2
(Browse shelf)
001159486
Available 001159486
Total holds: 0

Includes bibliographical references and index

Vol. 1, ISBN 0-07-054201-5, 316 p.; vol. 2, ISBN0-07-054203-3, 790 p.

Digitized

Basic Scientific Subroutines Volume I Contents Preface Chapter I Introduction 1. 2. 3. 4. 5. Scope Contents Structure Requirements Execution Speed 1 1 2 2 3 4 Chapter II Plotting Subroutines 1. 2. 3. One-Dimensional Data Plot Function Plotting Two-Dimensional Data Plot 5 6 13 16 Chapter III Complex Variables 1. 2. 3. 4. The Complex Plane Complex Variable Operations Powers and Roots of Z =X + iY Spherical Coordinate Conversion 24 24 31 38 47 Chapter N Vector and Matrix Operations 1. 2. Vector Operations Matrix Sums and Products 53 53 63 VIII 3. 4. 5. 6. 7. 8. 9. 10. Other Matrix Operations Matrix Coordinate Changes Determinants Matrix Inversion Solving Linear Sets of Equations Characteristic Polynomials and Eigenvalues Eigenvalues by the Power Method Matrix Exponentiation and Differential Equations 79 86 87 94 101 105 111 117 Chapter V Random Number Generators 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. The Uniform Distribution, RND The Linear Distribution The Normal Distribution The Poisson Distribution The Binomial Distribution The Exponential Distribution The Fermi Distribution The Cauchy Distribution The Gamma Distribution The Beta Distribution The Weibull Distribution 125 127 131 134 137 141 144 146 148 150 152 155 Chapter VI Basic Series Approximations 1. 2. 3. 4. 5. Taylor Series Expansions Approximate Series Expansions Variations on the Optimal Series Theme Least-Squares Regression Extensions 159 159 162 165 167 191 Appendix I Subroutine Cross Index A. Software Index (by number) B. Function Index Appendix II Subroutine Listings A. Full Listings of Demonstration and Subroutine Programs B. Compacted Listings 193 219 IX Appendix III Conversion to Other BASICs and Microsoft BASIC Program Listings 265 311 315 References Index Volume II Introduction 1 Chapter 1 Least-Squares Approximation General Introduction to Polynomial Approximations 1.1 First-Order Least Squares 1.2 Second-Order Least Squares 1.3 Nth-Order Least Squares 1.4 Multidimensional Least Squares 1.5 Least-Squares Fitting with Orthogonal Polynomials 1.6 1.7 Iterated Regression Parametric Least Squares 1.8 Extending the Use of Least Squares 1.9 1.10 Summary and Conclusion 7 7 16 24 31 45 56 65 75 82 87 Chapter 2 Se ries-Approximation Techniques Introduction 2.1 2.2 Taylor Series and Homer's Rule Asymptotic Series 2.3 2.3.1 The Bessel Function 2.3.2 The Chi-Square Distribution Functions 2.3.3 The Gamma Function 2.3.4 The Error Function 2.4 Chebyshev Polynomials 2.5 Economization 2.6 Reversion, Inversion, and Shifting 2.6.1 Polynomial Reversion 2.6.2 Polynomial Inversion 2.6.3 Shifting the Expansion Point Rational Polynomials 2.7 Infinite Products 2.8 Complex Series 2.9 2.10 Summary and Conclusion 89 89 93 102 103 108 118 119 123 130 142 142 148 155 159 166 169 174 X Chapter 3 Functional Approxima ti ons by Iteration and Recursion Introduction 3.1 Roots by Iteration 3.2 Tangent Iteration 3.3 Arctangent by Recursion 3.4 3.5 Arcsine by Recursion Elliptic Integrals by Recursion 3.6 Natural Logarithm by Recursion 3.7 Bessel Functions by Recursion 3.8 Orthogonal Polynomial Coefficients by Recursion 3.9 3.10 Summary and Conclusion 175 175 177 190 194 199 202 206 209 215 229 Chapter 4 CORDIC Approxima ti on Techniques and Alterna ti ves 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 Introduction The Trigonometric Functions Generating the T. and PN Coefficients The Inverse Trigonometric Functions The Exponential Function The Natural-Logarithm Function The Hyperbolic Trigonometric Functions Inverse Hyperbolic Trigonometric Functions 231 231 233 243 245 254 261 269 277 Chapter 5 Table Interpola ti on, Differentiation, and Integration 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 285 Introduction 285 Lagrange Interpolation 287 Newton Divided-Differences Interpolation and Error Estimates 293 Choosing the Table Values 300 Semi-Spline Interpolation 305 Calculating Derivatives from Tables 311 Table Integration 316 Interpolation and Integration of 2/\T e` 2 326 Summary and Conclusion 332 Chapter 6 Finding the Real Roots of Functions 6.1 6.2 333 Introduction 333 Gaining Preliminary Knowledge About the Roots of a Polynomial 335 xl 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14 6.15 6.16 340 Interval Searches Successive Substitution 348 Examples of Successive Substitution 352 Forcing the x = g(x) Form 362 Formalizing the Generation of x,, + 1 = g(x,,) 364 Newton's Method 366 The Secant and False-Position Methods 371 Numerical Comparisons of the Newton, Secant, and False-Position Methods 380 Aitken Acceleration 383 Aitken-Steffenson Iteration 393 Comparison of Algorithms 398 Finding More Roots: Multiplicity 399 Finding More Roots: Removal 401 Conclusion 411 Chapter 7 Finding the Complex Roots of Functions Introduction Review of the Fundamental Properties of Functions in the Complex Domain Interval Search 7.3 Newton's Method in the Complex Domain 7.4 Mueller's Method in One Dimension 7.5 7.6 Two-Dimensional Form of Mueller's Method Mueller's Method in the Complex Plane 7.7 7.8 Representing Polynomials in the µ(x, y) + i v(x,y) Form and Removing Roots 7.9 The Quadratic Formula Lin's Method 7.10 7.11 Bairstow's Method 7.12 Summary--Comparison of Algorithms 7.1 7.2 413 413 415 418 443 448 457 464 473 488 492 500 506 Chapter 8 Optimization by Steepest Descent 8.1 8.2 8.3 8.4 Introduction Steepest Descent with Functional Derivatives Steepest Descent with Approximate Derivatives Summary and Conclusions 509 509 512 519 531 XII References Appendix IA Software Index by Number Appendix IB Software Index by Function Appendix IIA Full Listings of North Star BASIC Demonstration and Subroutine Programs Appendix IIB Compacted North Star BASIC Subroutine Listing Appendix III Conversion to Other BASIC Dialects and Microsoft BASIC Program Listings Index 533 539 543 549 645 687 787

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