Abstract: Systems and methods are provided for generating multiple system state projections using a grid computing environment. A central coordinator software component executes on a root data processor and provides commands and data to a plurality of node coordinator software components. A node coordinator software component manages threads which execute on its associated node data processor and which perform a set of matrix operations. Stochastic simulations use results of the matrix operations to generate multiple state projections. Additional processing can be performed by the grid computing environment based upon the generated state projections, such as to develop possible change information for users.

Abstract: Systems and methods are provided for generating multiple system state projections for one or more scenarios using a grid computing environment. A central coordinator software component executes on a root data processor and provides commands and data to a plurality of node coordinator software components. A node coordinator software component manages threads which execute on its associated node data processor and which perform a set of matrix operations. Stochastic simulations use results of the matrix operations to generate multiple state projections. Additional processing can be performed by the grid computing environment based upon the generated state projections, such as to develop risk information for users.

Abstract: Systems and methods are provided for performing an estimation using an iteratively reweighted least squares technique on a scenario defined by a design matrix, a response variable vector, and a parameter to be estimated. A system and method can be configured to include a root data processor, where a least squares estimate is calculated by the root data processor during each of a plurality of processing iterations. A plurality of node data processors can also be configured to: update values of a weight matrix according to a current state of the least squares estimate, determine a first intermediate value based on the design matrix and the weight matrix, determine a second intermediate value based on the design and weight matrices and the response variable vector. The root data processor calculates an updated least squares estimate based on the intermediate values.

Abstract: Computer-implemented systems and methods for analyzing costs associated with a cost flow model having components of relationships and entities. A system and method can be configured to receive a data associated with the cost flow model as well as source-entity definitions, via-entity sets, and target-entity definitions. A set of linear equations is created that is representative of the costs and entity relationships, wherein data about certain relationships satisfying a removal criteria are not included in the matrices. The system of linear equations is solved to determine contribution values from the source entities to the target entities through the via-sets.

Abstract: A computer-implemented system and method are provided to handle operations dealing with a multidimensional database. Information about the hierarchical structure of a multidimensional database is used when performing the operations upon the database. Operations including update, select and others are performed using the hierarchical structural information. Keys and indexes are used in accessing the hierarchical structural information.

Abstract: Computer-implemented systems and methods for analyzing costs associated with a cost flow model having components of relationships and entities. A system and method can be configured to receive data associated with the cost flow model that identifies the costs associated with the relationships among the entities. One or more matrices are created that are representative of the costs and the entity relationships. One or more sparse matrix operations are performed upon the created one or more matrices in order to determine cost contribution amounts from an entity to another entity.

Abstract: Systems and methods are provided for generating multiple system state projections for one or more scenarios using a grid computing environment. A central coordinator software component executes on a root data processor and provides commands and data to a plurality of node coordinator software components. A node coordinator software component manages threads which execute on its associated node data processor and which perform a set of matrix operations. Stochastic simulations use results of the matrix operations to generate multiple state projections. Additional processing can be performed by the grid computing environment based upon the generated state projections, such as to develop risk information for users.

Abstract: Systems and methods are provided for performing an estimation using an iteratively reweighted least squares technique on a scenario defined by a design matrix, a response variable vector, and a parameter to be estimated. A system and method can be configured to include a root data processor, where a least squares estimate is calculated by the root data processor during each of a plurality of processing iterations. A plurality of node data processors can also be configured to: update values of a weight matrix according to a current state of the least squares estimate, determine a first intermediate value based on the design matrix and the weight matrix, determine a second intermediate value based on the design and weight matrices and the response variable vector. The root data processor calculates an updated least squares estimate based on the intermediate values.

Abstract: A computer-implemented system and method are provided to handle operations dealing with a multidimensional database. Information about the hierarchical structure of a multidimensional database is used when performing the operations upon the database. Operations such as update, select and others are performed using the hierarchical structural information. Keys and indexes may be used in accessing the hierarchical structural information.

Abstract: A computer-implemented system and method are provided to handle operations dealing with a multidimensional database. Information about the hierarchical structure of a multidimensional database is used when performing the operations upon the database. Operations such as update, select and others are performed using the hierarchical structural information. Keys and indexes may be used in accessing the hierarchical structural information.

Abstract: Computer-implemented systems and methods for analyzing costs associated with a cost flow model having components of relationships and entities. A system and method can be configured to receive a data associated with the cost flow model as well as source-entity definitions, via-entity sets, and target-entity definitions. A set of linear equations is created that is representative of the costs and entity relationships, wherein data about certain relationships satisfying a removal criteria are not included in the matrices. The system of linear equations is solved to determine contribution values from the source entities to the target entities through the via-sets.

Abstract: Computer-implemented systems and methods for analyzing costs associated with a cost flow model having components of relationships and entities. A system and method can be configured to receive data associated with the cost flow model that identifies the costs associated with the relationships among the entities. One or more matrices are created that are representative of the costs and the entity relationships. One or more sparse matrix operations are performed upon the created one or more matrices in order to determine cost contribution amounts from an entity to another entity.