the list of references is followed by a line of all dashes and then by a list of keywords for the algorithms. these keywords have been prepared from an understanding of the content of the algorithm. the keywords given might not have appeared with the primary publication. the keyword omit is given for algorithms which are considered to be trivial or obsolete for any but historical purposes. --------------------------------------------------------------------- the keywords are in the following format: algorithm number, algorithm classification according to the modified share scheme and the list of keywords (one per line after the first line). 493 c2 polynomial zeros 494 d3 partial differential equations method of lines ordinary differential equations 495 f4 chebyshev solution linear system linear programming simplex method 496 f2 eigenvalues generalized eigenvalue problem 497 d2 functional differential equations numerical integration one-step and multistep methods 498 s17 airy function chebyshev series approximation chebyshev coefficients asymptotic expansion taylor expansion 499 z pattern recognition partial differential equations finite differences laplace's equation 500 e4 minimization optimization 501 e2 approximation polynomial approximation exchange algorithm chebyshev approximation polynomial approximation 502 c5 nonlinear equations differentiation with respect to a parameter one-parameter embedding dependence on parameter 503 d5 linear integral equations nystrom method 504 d ordinary differential equations initial value problems global error estimation runge-kutta-fehlberg method 505 s2 sorting searching linked lists data structure list operation 506 f2 eigenvalues qr-algorithm 507 e1 approximation interpolation spline approximation quintic natural spline 508 f1 bandwidth reduction profile reduction sparse matrix 509 f1 bandwidth reduction king algorithm profile reduction sparse matrix approximation 510 e2 piecewise linear function 511 s18 bessel function of the first kind modified function airy function uniform asymptotic expansion 512 f4 linear function normalized solution periodic quindiagonal symmetric positive definite 513 f1 transposition in place matrix transposition permutation 514 e2 interpolation cubic splines spline approximation 515 g6 combinations 516 f2 confidence interval illinois method point estimate regula falsi wilcoxon-mann-whitney rank test 517 f2 eigenvalues condition number 518 s14 incomplete bessel function von mises distribution 519 s14 kolmogorov-smirnov probabilities 520 h resource allocation linear programming 521 s15 integral of the coerror function miller's recurrence algorithm 522 f4 symbolic and algebraic manipulation linear system congruence techniques 523 z partitioning sorting 524 a1 multiple precision extended precision floating arithmetic elementary function euler's constant gamma function bessel function exponential integral logarithmic integral bernoulli numbers zeta function 525 e2 spline approximation adaptive curve fitting hermite interpolation 526 e1 bivariate interpolation piecewise polynomial interpolation 527 d3 marching algorithms block tridiagonal matrix elliptic partial differential equations 528 z portability mathematical software libraries error handling storage management memory allocation machine dependencies 529 f1 symmetric permutations block triangular form depth first search algorithm sparse matrix 530 f2 eigenvalues eigenvectors skew-symmetric matrix symmetric matrix matrix with constant diagonal 531 j6 contour plotting 532 z automatic roundoff analysis numerical stability numerical linear algebra 533 f4 sparse matrix sparse matrix simultaneous linear equations partial pivoting algorithms 534 d2 stiff differential equations stiffly stable methods composite multistep methods cyclic methods numerical integration ordinary differential equations initial value problems multistep formulas numerical integration program 535 f2 eigenvalues generalized eigenvalue problem 536 z one-way security transformation password encipher decipher multiprecision integer arithmetic 537 s22 mathieu's differential equation wave equation characteristic values eigenvalues separation constants mathieu function ordinary mathieu function modified mathieu function elliptic cylinder function hyperbolic cylinder function 538 f2 eigenvalues eigenvectors sparse matrix diagonable matrix simultaneous iteration 539 f1 linear algebra utilities 540 d3 collocation methods partial differential equations numerical software method of lines 541 d3 elliptic partial differential equations software linear systems 542 s14 computation of incomplete gamma function taylor's series continued fractions 543 d3 fast fourier transform fast helmholtz solver fast poisson solver 544 f4 covariance matrix curve fitting iterative refinement least squares solution linear constraints overdetermined system of equations regression underdetermined system of equations 545 c6 multidimensional fft fast fourier transform fft mass storage fft mass store sorting optimal sorting 546 f4 almost block diagonal systems gaussian elimination spline approximation ordinary differential equations 547 e3 discrete splines discrete cubic splines discrete natural splines interpolation smoothing 548 h assignment problem hungarian algorithm 549 s21 weierstrass' elliptic function 550 z polyhedron graphics numerical integration 551 f4 overdetermined system of linear equations discrete linear l(sub 1) approximation linear programming duel simplex algorithm triangular decomposition 552 f4 constrained l(sub 1) approximation linear programming simplex method 553 d3 parabolic partial differential equations semidiscretization explicit time integrator 554 c5 nonlinear equations numerical solution brent's method 555 c5 fixed point zero nonlinear systems homotopy method continuation method parameterized nonlinear systems zero curve of a homotopy map fixed points of nonlinear systems zeros of nonlinear systems 556 s13 exponential integral miller algorithm confluent hypergeometric function 557 h goal program multiple objective optimization constraint partitioning simplex method 558 h multifacility optimal location rectilinear distance minimum cut 559 e4 quadratic programming orthogonal decomposition 560 f2 jordan normal form canonical form eigenvalues eigenvectors principal vectors block diagonal form 561 z heap table maintenance 562 h shortest path shortest route problem 563 f4 numerical analysis overdetermined linear systems linear constraints discrete l(sub 1) approximation 564 z l(sub 1) approximation least absolute deviation problem generator test data 565 d3 partial differential equations method of lines finite differences ordinary differential equations 566 c5 performance testing systems of nonlinear equations nonlinear least squares unconstrained minimization optimization software 567 a1 angular momentum extended-range arithmetic legendre polynomials overflow underflow 568 z file directory system unix ratfor 569 d2 ordinary differential equations boundary-value problems collocation boundary spline mesh selection error estimates damped newton's method general-purpose code 570 f2 eigenvalues eigenvectors simultaneous iteration real nonsymmetric matrix sparse matrix 571 s14 direction statistics von mises distribution fisher distribution modified bessel function ratio continued fraction function inversion newton-raphson methods 572 d3 helmholtz equation capacitance matrix fast poisson solver conjugate gradients 573 e4 unconstrained optimization nonlinear least squares nonlinear regression quasi-newton methods secant methods 574 e1 polynomial interpolation osculation shape preserving convexity preserving monotonicity preserving bernstein polynomial 575 f1 nonsymmetric permutations maximum transversal maximum assignment block triangular form sparse matrix 576 f4 simultaneous linear equations gaussian elimination new pivoting strategy 577 s21 elliptic integral logarithms inverse circular function inverse hyperbolic function r-function 578 f4 gaussian elimination paged virtual store 579 d4 numerical differentiation taylor series coefficients analytic function 580 f5 matrix factorization orthogonalization 581 f1 singular value decomposition 582 f4 matrix bandwidth matrix profile matrix wavefront banded matrix gibbs-poole-stockmeyer algorithm gibbs-king algorithm 583 g2 analysis of variance conjugate-gradient method least squares solution simultaneous linear equations regression sparse matrix 584 d1 quadrature rule 585 e1 convergence acceleration extrapolation interpolation least squares approximation neville-aitken scheme 586 f4 iterative methods numerical software sparse matrix 587 f4 linear least squares solution equality constraints inequality constraints nonnegativity constraints inconsistent constraints covariance matrix 588 z hankel transforms of integer order bessel function of the first kind convolution integral linear digital filters 589 f2 matrix eigensystems iterative method eigensystem improvement 590 f2 generalized eigenvalue qz algorithm 591 g2 linear models analysis of variance unbalanced data missing cells estimation hypothesis testing storage-efficient algorithm iterative improvement balanced data operators algebraic-model specification rank computations g-inverse solution 592 e2 optimal estimation optimal interpolation perfect splines 593 d3 helmholtz equation capacitance matrix fast poisson solvers conjugate gradients software package 594 z round-off analysis relative errors numerical stability 595 h hamiltonian circuit depth-first search 596 d2 equilibrium problems underdetermined systems of equations solution manifolds of parameterized equations continuation methods local parameterization limit point computation 597 s17 bessel function 598 f2 matrix equations solvent newton's method qz algorithm 599 g5 gamma distribution poisson distribution random numbers acceptance-rejection method simulation 600 e2 approximation interpolation spline approximation quintic natural spline 601 f1 sparse matrix 602 c6 acceleration of convergence transformation of divergent series levin's 'u' transform 603 f4 almost block and diagonal systems gaussian elimination alternate row and column elimination two-point boundary-value problems 604 c1 remes algorithm extremal polynomial richardson iteration 605 z verifiers standard conformance basic programming language 606 z expert systems menu-driven applications computer-aided instruction techniques 607 z text exchange text management text organization text distribution text maintenance 608 h assignment problem quadratic assignment heuristic algorithms operations research 609 s13 exponential integrals bickley functions integral of bessel function bessel function 610 s14 psi functions gamma function derivatives of the gamma function 611 e4 trust regions quasi-newton bfgs secant update finite differences reverse communication 612 d1 quadrature rule two dimensional integration singular integrands epsilon algorithm 613 h minimum spanning tree shortest connection network 614 d1 quadrature rule optimal quadrature rule singular integrands 615 g2 regression least absolute value