## Numerical Analysis: Mathematics of Scientific ComputingThis book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with appropriate motivations and careful proofs. In an engaging and informal style, the authors demonstrate that many computational procedures and intriguing questions of computer science arise from theorems and proofs. Algorithms are presented in pseudocode, so that students can immediately write computer programs in standard languages or use interactive mathematical software packages. This book occasionally touches upon more advanced topics that are not usually contained in standard textbooks at this level. |

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Nice book, actually, I am taking Kincaid's class right now.

### Contents

II | 3 |

III | 15 |

IV | 28 |

V | 37 |

VI | 55 |

VII | 64 |

VIII | 73 |

IX | 74 |

XLVII | 502 |

XLVIII | 507 |

XLIX | 513 |

L | 519 |

LI | 524 |

LII | 530 |

LIII | 539 |

LIV | 549 |

X | 81 |

XI | 93 |

XII | 100 |

XIII | 109 |

XIV | 130 |

XV | 139 |

XVI | 140 |

XVII | 149 |

XVIII | 163 |

XIX | 186 |

XX | 197 |

XXI | 207 |

XXII | 232 |

XXIII | 245 |

XXIV | 254 |

XXV | 257 |

XXVI | 265 |

XXVII | 273 |

XXVIII | 287 |

XXIX | 298 |

XXX | 308 |

XXXI | 327 |

XXXII | 338 |

XXXIII | 349 |

XXXIV | 366 |

XXXV | 377 |

XXXVI | 388 |

XXXVII | 392 |

XXXVIII | 405 |

XXXIX | 420 |

XL | 438 |

XLI | 445 |

XLII | 451 |

XLIII | 460 |

XLIV | 465 |

XLV | 478 |

XLVI | 492 |

LV | 557 |

LVI | 565 |

LVII | 572 |

LVIII | 581 |

LIX | 589 |

LX | 593 |

LXI | 597 |

LXII | 608 |

LXIII | 615 |

LXIV | 623 |

LXV | 629 |

LXVI | 634 |

LXVII | 642 |

LXVIII | 650 |

LXIX | 660 |

LXX | 667 |

LXXI | 676 |

LXXII | 681 |

LXXIII | 689 |

LXXIV | 695 |

LXXV | 700 |

LXXVI | 711 |

LXXVII | 712 |

LXXVIII | 716 |

LXXIX | 719 |

LXXX | 721 |

LXXXI | 722 |

LXXXII | 723 |

LXXXIII | 724 |

LXXXIV | 725 |

LXXXV | 726 |

LXXXVI | 727 |

LXXXVII | 731 |

LXXXVIII | 745 |

771 | |

### Common terms and phrases

algorithm analysis assume best approximation bisection method coefficients column Computer Problem continued fraction continuous convergence convex set cubic spline defined denoted derivatives Determine differential equation divided difference eigenvalues elements example factorization Find formula Gaussian elimination given grid Hence inequality initial-value problem inner product inner-product space integral interpolating polynomial interval inverse iteration knots Lemma linear function lower triangular m x n machine numbers mathematical matrix norm n x n matrix Newton's method nodes nonsingular nonzero numerical solution obtain orthogonal orthonormal polynomial of degree positive definite preceding problem procedure Prove pseudocode pseudoinverse quadratic real number result roots roundoff error Runge-Kutta Runge-Kutta method satisfy secant method Section sequence Show singular-value decomposition solve space step subspace Suppose system of equations Taylor series Taylor's Theorem THEOREM 1 Theorem truncation error upper triangular values variables vector write zero