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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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 initialvalue problem inner product innerproduct 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 RungeKutta RungeKutta method satisfy secant method Section sequence Show singularvalue 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