Information-Based Complexity

Iterative Methods for the Solution of Equations.

1967 • 2,190 citations

Sequential minimax search for a maximum

1953 • 949 citations

Gaussian measures in Banach spaces

1975 • 924 citations

A Fast Monte-Carlo Test for Primality

1977 • 648 citations

A General Theory of Optimal Algorithms

1980 • 615 citations

Problem Complexity and Method Efficiency in Optimization

1984 • 603 citations

Integration in Hilbert Space

1974 • 394 citations

Deterministic and Stochastic Error Bounds in Numerical Analysis

1988 • 372 citations

The fundamental theorem of algebra and complexity theory

1981 • 362 citations

A Survey of Optimal Recovery

1977 • 329 citations

Monte-Carlo algorithms for enumeration and reliability problems

1983 • 314 citations

Sequential Minimax Search for a Maximum

1953 • 277 citations

On the average number of steps of the simplex method of linear programming

1983 • 276 citations

Estimating the Largest Eigenvalue by the Power and Lanczos Algorithms with a Random Start

1992 • 270 citations

Optimal algorithms theory for robust estimation and prediction

1985 • 251 citations

An upper and lower bound for clock synchronization

1984 • 250 citations

Best Approximate Integration Formulas; Best Approximation Formulas

1949 • 214 citations

Coping with errors in binary search procedures

1980 • 189 citations

Families of Rational Maps and Iterative Root-Finding Algorithms

1987 • 177 citations

Effective Price Mechanisms

1978 • 161 citations

A new fault-tolerant algorithm for clock synchronization

1984 • 153 citations

MULTIPLE-PRECISION ZERO-FINDING METHODS AND THE COMPLEXITY OF ELEMENTARY FUNCTION EVALUATION

1976 • 145 citations

Error Bounds for Gaussian Quadrature of Analytic Functions

1983 • 135 citations

A simplex algorithm whose average number of steps is bounded between two quadratic functions of the smaller dimension

1985 • 133 citations

On Algorithms for Solving f(x)=0

1979 • 128 citations

On the optimality of linear methods for operator approximation in convex classes of functions

1971 • 101 citations

Computational Complexity: On the Geometry of Polynomials and a Theory of Cost: II

1986 • 96 citations

Approximation of linear functionals on a banach space with a Gaussian measure

1986 • 95 citations

Bisection is optimal

1982 • 92 citations

Computing the topological degree of a mapping inR n

1975 • 88 citations

Optimum Sequential Search and Approximation Methods Under Minimum Regularity Assumptions

1957 • 86 citations

Optimal sequential and non-sequential procedures for evaluating a functional

1980 • 85 citations

A bisection method for systems of nonlinear equations

1984 • 79 citations

Can adaption help on the average?

1984 • 78 citations

Monte-Carlo algorithms for the planar multiterminal network reliability problem

1985 • 74 citations

On irregularities of distribution

1980 • 72 citations

Average case optimal algorithms in Hilbert spaces

1986 • 68 citations

Error estimates for Gauss quadrature formulas for analytic functions

1968 • 63 citations

ON A THEORY OF COMPUTATION AND COMPLEXITY OVER THE REAL NUMBERS: NP-COMPLETENESS, RECURSIVE FUNCTIONS AND UNIVERSAL MACHINES

2000 • 60 citations

Noncomputability in analysis and physics: A complete determination of the class of noncomputable linear operators

1983 • 60 citations

s-Numbers in information-based complexity

1990 • 57 citations

Computational Complexity and Numerical Stability

1975 • 57 citations

Systematic Search in High Dimensional Sets

1977 • 55 citations

Exactness conditions in numerical quadrature

1964 • 55 citations

Complexity of Solving Linear Systems in Different Models of Computation

1984 • 48 citations

Linear problems (with extended range) have linear optimal algorithms

1986 • 45 citations

The Computational Complexity of Differential and Integral Equations

1991 • 43 citations

How to increase the order to get minimal-error algorithms for systems of ODE

1984 • 38 citations

Optimal iterative processes for root-finding

1972 • 36 citations

Asymptotic error estimates for the Gauss quadrature formula

1968 • 34 citations

Information-Based Complexity

1986 • 34 citations

On the existence of generally convergent algorithms

1986 • 32 citations

Computational Complexity of Iterative Processes

1972 • 31 citations

On the Optimal Solution of Large Linear Systems

1984 • 31 citations

Optimal error and GMDH predictors

1987 • 30 citations

On optimality of Krylov's information when solving linear operator equations

1991 • 26 citations

THE COMPLEXITY OF OBTAINING STARTING POINTS FOR SOLVING OPERATOR EQUATIONS BY NEWTON'S METHOD

1976 • 26 citations

Recent developments in information-based complexity

1987 • 24 citations

An algorithm for numerical calculation of topological degree

1979 • 24 citations

Is Gauss quadrature optimal for analytic functions?

1985 • 24 citations

On the existence of optimal integration formulas for analytic functions

1974 • 24 citations

Computing the degree of maps and a generalized method of bisection

1977 • 22 citations

A three-dimensional analogue to the method of bisections for solving nonlinear equations

1979 • 22 citations

Asymptotic properties of minimum norm and optimal quadratures

1968 • 22 citations

A simplification of Stenger's topological degree formula

1979 • 21 citations

Optimal quadrature ofH p functions

1980 • 21 citations

Quadratures with remainders of minimum norm. II

1967 • 21 citations

Elliptically contoured measures on infinite-dimensional Banach spaces

1977 • 21 citations

On the construction of sufficient refinements for computation of topological degree

1981 • 20 citations

MAXIMAL ORDER OF MULTIPOINT ITERATIONS USING n EVALUATIONS

1976 • 19 citations

On the minimal cost of approximating linear problems based on information with deterministic noise

1990 • 18 citations

High Order Search Methods for Finding Roots

1975 • 16 citations

On the optimality of Krylov information

1987 • 16 citations

STRICT LOWER AND UPPER BOUNDS ON ITERATIVE COMPUTATIONAL COMPLEXITY

1976 • 16 citations

On sequential and parallel solution of initial value problems

1990 • 16 citations

Complexity of computing topological degree of lipschitz functions in n dimensions

1986 • 16 citations

Optimal algorithms for image understanding: Current status and future plans

1985 • 13 citations

Optimal search for the roots of a function satisfying a lipschitz condition

1976 • 13 citations

Asymptotic error of algorithms for solving nonlinear problems

1987 • 13 citations

How powerful is continuous nonlinear information for linear problems?

1986 • 13 citations

On the optimal error of algorithms for solving a scalar autonomous ode

1982 • 13 citations

Average complexity for linear operators over bounded domains

1987 • 12 citations

Information-based numerical practice

1987 • 12 citations

Optimal Quadratures in $L^2 (E_\rho )$. I

1967 • 11 citations

On functional iteration and the calculation of roots

1961 • 11 citations

Sequential minimax search for a zero of a convex function

1959 • 11 citations

Global Convergence of a Modified Newton Iteration for Algebraic Equations

1982 • 11 citations

An optimal algorithm for finding the roots of an approximately computed function

1968 • 11 citations

Asymptotic near optimality of the bisection method

1990 • 11 citations

Properties of optimal methods for the solution of problems of mathematical physics

1970 • 9 citations

Optimality of Euler-integral information for solving a scalar autonomous ode

1983 • 9 citations

On the optimal solution of large eigenpair problems

1986 • 9 citations

Solving Linear Equations by Means of Scalar Products

1972 • 8 citations

On the Power of Adaptive Information for Functions with Singularities

1992 • 7 citations

On Optimal Algorithms in an Asymptotic Model with Gaussian Measure

1988 • 7 citations

Asymptotic minimum norm quadrature formulae

1975 • 7 citations

Adaption helps for some nonconvex classes

1986 • 7 citations

THE USE OF INTEGRALS IN THE SOLUTION OF NONLINEAR EQUATIONS IN N DIMENSIONS

1976 • 6 citations

Convergence and complexity of interpolatory—newton iteration in a Banach space

1980 • 6 citations

Can we approximate zeros of functions with nonzero topological degree?

1988 • 6 citations

An Error Analysis for Interpolation of Analytic Functions

1968 • 5 citations

A clock synchronization problem with random delays

1989 • 5 citations

On the Existence of Generally Convergent Algorithms

2000 • 2 citations

Tight bounds on the complexity index of one-point iterations

1980 • 2 citations

Some Basic Information on Information-Based Complexity Theory

1989 • 2 citations

Deleted Work

1955 • 0 citations